AP Physics C: Electricity and Magnetism FRQ Room

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AP Physics C: Electricity and Magnetism Free Response Questions

The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics C: Electricity and Magnetism FRQs to get ready for the big day.

  • View all (250)
  • Unit 1: Electrostatics (56)
  • Unit 2: Conductors, Capacitors, Dielectrics (38)
  • Unit 3: Electric Circuits (45)
  • Unit 4: Magnetic Fields (57)
  • Unit 5: Electromagnetism (54)
Unit 1: Electrostatics

Analysis of Discharging Capacitor in an RC Circuit using Calculus

Design an experiment to study the discharging behavior of a capacitor in an RC circuit. Measure the

Medium

Analyzing Electric Field Inside a Uniformly Charged Sphere

Design an experiment to measure the electric field at various points inside a uniformly charged insu

Hard

Assessing the Impact of Charge Magnitude Variation on Force Measurements

An experiment is designed where the charge on a test object can be varied systematically. The hypoth

Easy

Calculus-Based Analysis of Electric Field from a Given Potential Function

Given a specified electric potential function along the x-axis, use calculus to determine the associ

Hard

Calibrated Probe Measurements of Electric Field Strength in a 2D Plane

A set of calibrated probes measures the electric field at various (x, y) positions within a planar r

Hard

Capacitor Charging in an RC Circuit

A capacitor with capacitance $$C$$ is charged through a resistor $$R$$ by a constant voltage source

Medium

Capacitor with Dielectric Insertion

This problem examines how the capacitance and stored energy of a parallel plate capacitor change whe

Easy

Charge Conservation and Electrostatic Interactions

Charge conservation and electrostatic interactions are fundamental concepts in electromagnetism. Dis

Easy

Comparative Analysis of Conductors and Insulators

An experiment compares the charge retention in a conductor versus an insulator when both are initial

Medium

Deriving Electric Potential from a Sinusoidal Electric Field

The electric field in a region is given by $$E(x) = 500 * \sin(2*x)$$ N/C, where x is in meters. (a)

Hard

Designing an Experiment to Measure the Electric Field due to a Cylindrical Charge Distribution

Design an experiment to measure the electric field around a long, uniformly charged cylinder using a

Hard

Determining Electric Potential from a Given Field

Here, you are given an electric field expressed as a function of position and are asked to derive th

Medium

Dynamics of a Charged Particle in a Non-Uniform Electric Field

A charged particle of mass m and charge q enters a region where the electric field decreases with di

Hard

Electric Field Along the Axis of a Charged Ring

A thin ring of radius $$R$$ carries a uniform charge Q distributed evenly along its circumference. D

Easy

Electric Field and Potential Gradient

This question deals with the relationship between electric potential and the electric field in the v

Medium

Electric Field Behavior in a Uniformly Charged Sphere

A uniformly charged sphere with radius 0.25 m is examined. The electric field strength is measured a

Hard

Electric Field Due to a Point Charge

A point charge of $$+2.0*10^{-9} \; C$$ is located at the origin in a vacuum. Answer the following:

Easy

Electric Field from a Continuous Charge Distribution: Charged Rod

A uniformly charged rod of length $$L$$ and total charge $$Q$$ creates an electric field along its a

Hard

Electric Field from a Cylindrical Charge Distribution

An infinitely long cylindrical rod of radius $$R = 0.05 \; m$$ carries a uniform volume charge densi

Extreme

Electric Field from a Uniformly Charged Rod

A researcher is studying the electric field produced by a thin rod of length $$L$$, uniformly charge

Medium

Electric Field from an Extended Linear Charge Distribution

A thin rod of length $$L = 0.50 \; m$$ has a uniform linear charge density $$\lambda = 2.0*10^{-8} \

Hard

Electric Field from an Infinite Plane of Charge

A large, flat surface carries a uniform surface charge density of $$\sigma = 3.0*10^{-6} \; C/m^2$$.

Medium

Electric Field Inside a Uniformly Charged Sphere

A nonconducting sphere of radius $$R = 0.20 \; m$$ carries a uniformly distributed charge $$Q = +5.0

Medium

Electric Field of a Conducting Sphere

A conducting sphere of radius R is uniformly charged with total charge Q. Answer the following quest

Easy

Electric Field of a Planar Charge Distribution and Edge Effects

A researcher analyzes the electric field produced by a uniformly charged infinite plane and compares

Hard

Electric Flux and Gauss' Law in Different Geometries

Students conduct a computer simulation of electric flux through various closed surfaces, including a

Medium

Electric Force Between Point Charges

This question addresses the calculation of the electrostatic force between two point charges using C

Medium

Electric Potential and Field from a Point Charge

A point charge of 5 ÎźC is located at the origin. (a) Write the expression for the electric potential

Medium

Electric Potential Energy in a System of Charges

Consider a system of point charges. Explore the concept of electric potential energy within this sys

Medium

Electrostatic Force Variation with Distance

An experiment is conducted to verify Coulomb's law by measuring the force between two point charges

Easy

Energy Considerations in Bringing Charges from Infinity

Analyze the work done by an external agent in assembling a two-charge system from infinity to a fini

Hard

Evaluating the Charge on a Sphere using Measured Electric Field Data

This problem starts with experimental data of the radial electric field from a charged sphere and as

Hard

Evaluating the Effects of Dielectric Materials on a Capacitor

In this problem, you will derive the capacitance of a parallel plate capacitor both in vacuum and wh

Medium

FRQ 4: Analysis of Non-Uniform Electric Field in a Laboratory Setup

A student reports that their electric field measurements in a region with multiple charge sources sh

Hard

FRQ 16: Critical Evaluation of Voltage Measurements in a Capacitor

A recent study claims that a new technique for measuring voltage across capacitor plates produces si

Medium

Gauss' Law for a Non-Uniform Spherical Charge Distribution

Consider a sphere of radius R with a radial dependent charge density given by $$\rho(r) = \rho_0*(r/

Hard

Gauss’s Law in a Uniformly Charged Sphere

A non‐conducting sphere of radius R = 0.5 m carries a uniformly distributed charge Q = 1.0×10⁻⁶ C. U

Easy

Integrating Charge Density to Determine Total Charge in a Spherical Volume

In an experiment, the volume charge density inside a sphere is modeled by ρ(r) = ρ₀ e^(-r), where ρ₀

Extreme

Integration to Determine Electric Potential along a Line

A uniformly charged rod creates an electric potential along its axis. Determine this potential using

Hard

Investigating Electric Fields in Conductors vs. Insulators

Design an experiment to compare the electric field distribution around a metallic (conductor) sphere

Medium

Investigating the Relationship between Electric Flux and Surface Geometry

A simulation is designed to explore how electric flux through a surface depends on the geometry of t

Medium

Measuring Electric Field Lines using Near-field Probes

In this experiment, a set of movable near-field probes is used to measure the spatial variation of t

Hard

Measuring the Polarization Effects in an Insulating Material

An experiment is set up to study polarization in an insulating material. The material is placed in a

Extreme

Multi-Charge Interaction Analysis

Three point charges are located at the vertices of an equilateral triangle with side length $$0.10 \

Hard

Non-Uniform Charge Distribution in a Sphere

Consider a sphere of radius $$R$$ in which the volume charge density varies with radius as $$\rho(r)

Extreme

Optimization of Non-uniform Charge Distribution

A researcher aims to optimize the electric field at a point P on the y-axis (distance $$d$$ from the

Extreme

Point Charge Interaction Experiment

Two point charges are fixed in space, and an experiment is carried out to measure the force experien

Medium

Point Charge Interactions and Coulomb's Law

Two point charges are placed along the x-axis in a vacuum. Let $$q_1 = +1.602*10^{-19} \; C$$ be loc

Easy

Point Charge Potential Calculation

Consider a point charge of $$Q = 4.00 \; \mu C$$. (a) Derive the expression for the electric potent

Easy

Point Charges and Coulomb's Law Analysis

Consider two point charges placed along a horizontal line. Use Coulomb's law to analyze the interact

Easy

Transient Behavior in an RC Circuit

A researcher studies the transient discharge of a capacitor in an RC circuit.

Easy

Uniform Electric Field in a Finite Charged Plate Experiment

An experiment is designed to verify the existence of a uniform electric field produced by a large, f

Hard

Work Done by a Uniform Electric Field

This problem examines the work done on a charged particle as it moves in a uniform electric field an

Easy

Work Done by Electric Fields in a Particle Accelerator

In designing a particle accelerator, a researcher wants to determine the work done by a constant ele

Easy

Work Done in a Non-Uniform Electric Field

This question requires you to compute the work done on a charge moving through a spatially varying (

Hard

Work Done Moving a Charge in a Point Charge Field

A charge q is moved in the electric field of a point charge Q from a distance r₁ to r₂. Using calcul

Medium
Unit 2: Conductors, Capacitors, Dielectrics

Analysis of Capacitors in Series and Parallel

A circuit contains three capacitors arranged such that capacitors $$C_1$$ and $$C_2$$ are connected

Medium

Analyzing Charge Distribution on a Composite Conductor

A researcher explores a composite conductor comprising regions with different curvatures and materia

Hard

Analyzing Dielectric Constant Influence on Capacitance

When a dielectric is inserted into a capacitor, its capacitance increases. Consider the following ta

Easy

Capacitive Sensor Response

A capacitive sensor is designed to measure tiny changes in the distance between its parallel plates.

Medium

Capacitor as a Pressure Sensor

A parallel plate capacitor is used as a pressure sensor. When pressure is applied, one of the plates

Medium

Capacitor Charging and Discharging in an RC Circuit

In a series RC circuit, a capacitor with capacitance \(C\) is charged by a constant voltage source \

Medium

Capacitor with Layered Dielectrics

A parallel plate capacitor is constructed using two different dielectric layers arranged in series.

Medium

Comparative Analysis of Capacitor Types in High Frequency Circuits

A study was performed to compare different types of capacitors—ceramic, electrolytic, film, and tant

Medium

Composite Dielectric Capacitor Analysis

A capacitor is built with two different dielectric layers in series. The first layer has thickness \

Hard

Curvature Effects on Conductor Electric Field Distribution

The electric field on the surface of a conductor is influenced by its local curvature. In a simplifi

Extreme

Deriving the Zero Electric Field Inside a Conductor

Use Gauss’ law and the boundary conditions at the surface of a conductor to prove that the electric

Easy

Designing a Faraday Cage for Sensitive Instrumentation

A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo

Medium

Determining Dielectric Constant Experimentally

In an experiment, a set of identical parallel plate capacitors is assembled with different dielectri

Medium

Dielectric Strength and Material Breakdown Analysis

A capacitor with a dielectric material of thickness \(d\) is subject to an electric field. The diele

Easy

Dynamic Parallel Plate Capacitor

A parallel plate capacitor is charged to a constant charge $$Q$$ but has a plate separation that inc

Hard

Effect of Dielectrics on Capacitance

A capacitor initially in vacuum with capacitance $$C_0$$ has a dielectric material with dielectric c

Medium

Effect of Dielectrics on Capacitance: A Comparative Study

A researcher investigates the effect of different dielectric materials on the capacitance of a paral

Easy

Electric Shielding Efficiency in a Laboratory Setting

A researcher tests the effectiveness of different conductive materials as electric shields. The shie

Medium

Energy Loss Due to Dielectric Heating in AC Capacitor Circuit

In an AC circuit containing a capacitor with a dielectric, experimental data were collected to measu

Extreme

Experimental Analysis of Dielectric Breakdown

A researcher investigates the dielectric strength of several insulating materials. The experiment in

Hard

FRQ 3: Charging and Discharging of a Parallel Plate Capacitor

In a laboratory experiment, students measure the voltage across a parallel plate capacitor in an RC

Hard

FRQ 7: Capacitor Discharge with a Time-Dependent Resistor

In an experimental circuit, a capacitor of capacitance $$C$$ is discharged through a resistor whose

Extreme

FRQ 10: Charge Distribution on Curved Conductors

An experiment is undertaken to measure the electric field strength at various points on an irregular

Medium

FRQ 10: Dielectric Constant Measurement in a Variable Dielectric Setup

In an experiment designed to measure the dielectric constant of a material, a partially inserting di

Hard

FRQ 12: Non-Uniform Charge Distribution on an Irregular Conductor

In this experiment, a researcher attempted to measure the charge distribution on an irregularly shap

Hard

FRQ 13: Theoretical Analysis of Electric Field Shielding in Layered Conductors

Multiple concentric conductive shells are used to shield a sensitive instrument from external electr

Medium

FRQ 20: Experimental Analysis of Dielectric Breakdown in Capacitors

A laboratory experiment was set up to determine the breakdown voltage of a dielectric material in a

Extreme

Investigation of a Variable Capacitor

A variable capacitor is tested by adjusting its knob position, and the corresponding capacitance is

Medium

Investigation of Dielectric Breakdown Voltage

A study was conducted to investigate the breakdown voltage of dielectric materials. The breakdown vo

Hard

Modeling Electric Field Interactions Between Two Conductors

When two conductors are placed in close proximity, their electric fields interact. Design an experim

Extreme

Modeling the Impact of an External Electric Field on a Capacitor with a Dielectric Insert

A researcher examines how an external uniform electric field influences the effective capacitance of

Extreme

Parallel Plate Capacitor with Gradually Varying Dielectric

Consider a parallel plate capacitor with plate area $$A$$ and separation $$d$$, where the dielectric

Extreme

Parallel Plate Capacitor with Non-uniform Plate Separation

A parallel plate capacitor has one plate fixed while the other plate is slightly curved so that the

Hard

RC Circuit Transient Analysis

A capacitor with capacitance $$C$$ is connected in series with a resistor $$R$$ and a constant volta

Hard

RC Circuit: Charging and Discharging Analysis with Differential Equations

In an RC circuit, a capacitor charges through a resistor from a DC source. Develop and solve the dif

Hard

RC Circuit: Charging and Discharging Capacitor Analysis

A capacitor is charged through a resistor from a constant voltage source and then allowed to dischar

Medium

Surface Charge Redistribution on Irregularly Shaped Conductors

An irregularly shaped conductor has varying curvature along its surface, leading to a non-uniform su

Extreme

Time-Dependent Dielectric Breakdown Analysis

A dielectric material of thickness $$d$$ has a breakdown electric field strength $$E_{break}$$. In r

Medium
Unit 3: Electric Circuits

Analysis of a Triangular Wave from a Function Generator

A function generator outputs a triangular wave defined by $$V(t)=12*(2*abs((t \mod 1)-0.5)-1)$$, whe

Medium

Analysis of AC Circuit Frequency Effects

In an AC circuit, the voltage is described by $$V(t) = V_0 \sin(2\pi f t)$$ with $$V_0 = 10\,V$$ and

Hard

Analysis of Power Supply Stability

Examine a power supply circuit where the output voltage is affected by varying load conditions. Use

Hard

Analyzing Temperature Effects on a Thermistor in a Circuit

A thermistor is used in a sensing circuit, and its resistance varies with temperature. The table bel

Medium

Analyzing the Effect of Temperature on Resistivity in a Circuit

A conductor's resistance varies with temperature according to the formula $$R = R_0 (1+ \alpha (T-T_

Hard

Application of Kirchhoff’s Current Law at a Complex Node

At a junction with multiple branches, apply Kirchhoff’s Current Law (KCL) and explore the implicatio

Easy

Applying Kirchhoff's Current Law in a Multi-Branch Network

A complex circuit node has three branches with currents measured experimentally. Use Kirchhoff's Cur

Medium

Battery EMF and Terminal Voltage Analysis

A non-ideal battery has an electromotive force (EMF) of 9 V and an internal resistance of 1 Ί. It is

Medium

Battery EMF with Time-Varying Load

A battery with an electromotive force (EMF) of 9 V and an internal resistance of 0.5 Ί is connected

Medium

Capacitors in Series: Voltage Division Analysis

A series circuit contains three capacitors with values $$C_{1}=2\,\mu F$$, $$C_{2}=3\,\mu F$$, and $

Medium

Characterizing a Non-Ideal Battery from Experimental Data

A researcher collects data on a battery’s performance by measuring its terminal voltage under variou

Medium

Complex Circuit Analysis using Kirchhoff’s Laws

Consider a circuit with three nodes where one resistor has a time-varying resistance given by $$R(t)

Extreme

Effect of Temperature on Resistor Resistance

A resistor's resistance varies with temperature as $$R(T)=R_0*(1+\alpha*(T-T_0))$$, where $$R_0=50\;

Hard

Energy Storage in Capacitors and Inductors

Using calculus, derive the expressions for the energy stored in (a) a capacitor with capacitance C c

Easy

Evaluating Measurement Errors in Circuit Instruments

Measurement errors in electrical instruments can propagate through calculations. Evaluate the error

Medium

Evaluating Power and Efficiency in an Electric Motor Circuit

This question assesses your understanding of power calculations in electrical circuits and your abil

Hard

Frequency Dependence of Capacitive Reactance

Investigate how the capacitive reactance in an AC circuit depends on frequency, and use calculus to

Medium

FRQ 1: Basic Circuit Calculations Using Ohm's Law

A simple circuit consists of a battery and a single resistor. The battery provides a voltage of $$12

Easy

FRQ 4: Power in a Circuit and Calculus Derivation

Consider a circuit with a resistor connected to a $$24\,V$$ battery and a resistor of $$8\,\Omega$$.

Easy

FRQ 7: Kirchhoff's Voltage Law in a Multi-Loop Circuit

A circuit consists of two loops that share a common resistor. The circuit has two voltage sources: $

Hard

Ideal Versus Non-Ideal Circuit Component Analysis

Theoretical models using ideal circuit components often predict behavior that deviates from experime

Extreme

Impact of Temperature on Resistance

Resistance in a conductor can change with temperature. Investigate this variation and its implicatio

Medium

Impedance Measurement in AC Circuits with Ignored Inconsistent Source Behavior

An experiment is conducted to measure the impedance of a complex AC circuit at various frequencies.

Hard

Investigating Temperature-Dependent Resistance of a Thermistor

This question explores how the resistance of a thermistor varies with temperature, requiring both ma

Hard

Kirchhoff’s Laws in Multi-loop Circuits

Design a circuit that consists of two loops which share a common resistor. The circuit includes two

Medium

Kirchhoff's Voltage Law in a Complex Circuit

Consider a circuit where three resistors (R1, R2, and R3) are connected in series with a battery of

Hard

Low-Pass Filter Analysis in an RC Circuit

An RC circuit is configured as a low-pass filter. Analyze its transfer function and cutoff frequency

Easy

Measuring Power Dissipation in Resistive Circuits

This question examines the derivation of power relationships in resistive circuits and requires you

Medium

Multi-Concept Analysis of Circuit Behavior Under Variable Conditions

A circuit comprises a non-ideal battery with an EMF of $$15\,V$$ and an internal resistance of $$0.8

Extreme

Multi-Loop Circuit Analysis using Kirchhoff's Laws

A circuit consists of two loops that share a common resistor. A student claims that by applying Kirc

Hard

Non-Ideal Battery EMF Measurement with Internal Resistance Error

A researcher attempts to measure the electromotive force (EMF) of a battery by connecting a voltmete

Hard

Parallel Circuit Current Distribution Error Analysis

A student conducts an experiment on a parallel resistor network powered by a constant voltage source

Medium

Power Consumption in a Resistor Under Time-Varying Voltage

A student conducts an experiment on a resistor and claims that the power consumption follows the for

Medium

Power Dissipation and Energy in a Resistive Circuit

A resistive circuit is powered by a constant current source. Examine the energy transfer in the resi

Medium

Power Dissipation and Non-Ideal Battery Analysis

Examine a circuit where a non-ideal battery with an electromotive force (EMF) of $$\mathcal{E} = 12\

Hard

RC Circuit Transient Analysis

An RC circuit is constructed with a resistor \(R = 2.0\,\Omega\) and a capacitor \(C = 5.0 \times 10

Hard

Resonance and Quality Factor in an LCR Circuit

A researcher examines an LCR series circuit comprising an inductor $$L=0.1\,H$$, a capacitor $$C=100

Extreme

Resonance in an RLC Circuit

Consider a series RLC circuit with $$R = 15\,\Omega$$, $$L = 0.2\,H$$, and $$C = 50\,\mu F$$ powered

Extreme

Series Circuit Analysis with Calculus Application

A researcher is investigating a series circuit in which three resistors (with initial values $$R_{1}

Medium

Solving a Differential Equation in a Series RLC Circuit

In a series RLC circuit, the current is governed by the differential equation $$L*\frac{d^2I}{dt^2}+

Hard

Temperature Effects on Conductor Resistance and Circuit Current

A researcher studies how temperature affects the resistance of a conductor. The resistance is given

Medium

Temperature Effects on Resistance

A researcher investigates how temperature affects the resistance of a thermistor. The experiment mea

Hard

Transient Analysis in an RL Circuit

A circuit comprising a resistor and an inductor (an RL circuit) is subject to a DC voltage step. Ana

Medium

Transient Response in a Non-Ideal RLC Filter

A series RLC circuit is used as a filter in which transient responses are critical. Analyze the circ

Extreme

Transient Response of an RC Circuit

An RC circuit with a resistor \(R = 10\,\Omega\) and a capacitor \(C = 2\times10^{-3}\,F\) is connec

Medium
Unit 4: Magnetic Fields

Analysis of Forced Oscillations in a Magnetic Pendulum

A novel experiment involves a magnetic pendulum oscillating within a time-varying external magnetic

Extreme

Analysis of Magnetic Flux in a Rotating Loop

A single-turn loop of area A is rotating in a uniform magnetic field of strength B with a constant a

Hard

Application of the Right-Hand Rule

A straight, horizontal wire carries a current of $$5 * A$$ from left to right. Using the right-hand

Easy

Calculating Magnetic Effects of a Time-Varying AC Current in a Circular Loop

A circular loop of wire carrying an alternating current is used in an induction system. The current

Extreme

Calculating Magnetic Field from a Wire with Non-uniform Current Density

A long, thin wire has a current density that varies along its length according to $$J(x) = J_0(1 + 0

Extreme

Calculus in Magnetic Induction: Time-Varying Current Effects

A solenoid with 400 turns over a length of 0.8 m is driven by a time-varying current expressed as $$

Hard

Comparison of Magnetic Fields from Different Geometries

A researcher compares the magnetic fields produced by different geometries – a straight wire, a circ

Medium

Critical Analysis of Ampère's Law in a Non-Uniform Magnetic Field

An experiment uses a loop to measure the magnetic field in a region where the field is non-uniform.

Extreme

Derivation of Ampère’s Law via Loop Integration

Consider a long straight wire carrying a constant current I. Derive Ampère’s Law for a circular loop

Extreme

Designing a Magnetic Crane with Controlled Current

A magnetic crane used in industrial lifting uses large current-carrying conductors to generate a str

Hard

Designing a Magnetic Levitation System

An engineer designs a magnetic levitation system where a current-carrying wire is used to levitate a

Extreme

Designing an Electromagnetic Levitation System

An engineering team is developing an electromagnetic levitation system for a high-speed train. The c

Extreme

Determining Torsional Stiffness from Angular Deflection Data

A metal wire is twisted by applying varying torques. The resulting angular deflection (in radians) w

Medium

Determining Torsional Stiffness from Magnetic Torque Data

A thin wire is subjected to magnetic torque in a uniform magnetic field, resulting in an angular dis

Medium

Determining Torsional Stiffness Using Magnetic Torque

A current-carrying wire is twisted by an external magnetic field, generating a measurable torque. (

Medium

Effect of Magnetic Field Direction Change on a Moving Charged Particle

Design an experiment to study the effect of changing the direction of a magnetic field on the deflec

Hard

Effect of Wire Orientation on Lorentz Force

A current-carrying wire oriented at different angles relative to a uniform magnetic field experience

Easy

Evaluating Magnetic Field Distribution in a Halved Solenoid

A long solenoid is physically divided into two equal halves. (a) Using integration, derive express

Medium

Evaluating the Applicability of the Biot-Savart Law

A recent paper asserts that the Biot-Savart Law, given by \(\vec{B} = \frac{\mu_0}{4 * \pi} \int \fr

Medium

Evaluation of Magnetic Field Produced by Parallel Current-Carrying Wires

In a lab experiment, two parallel wires carrying identical currents are set up with variable spacing

Hard

Experimental Study of the Interaction between Electric and Magnetic Forces on a Current-Carrying Wire

A student designs an experiment to measure the net force on a current-carrying wire placed in overla

Hard

Force Between Parallel Current-Carrying Wires

Two parallel wires, separated by a distance of 5.0 cm, are both carrying a current of 3 A. The curre

Easy

Force Between Parallel Current-Carrying Wires

Two long, parallel wires are separated by 0.05 m. Wire 1 carries a current of 7.0 A and Wire 2 carri

Medium

Force Between Two Parallel Current-Carrying Wires

A study claims that the attractive force per unit length between two parallel wires carrying current

Medium

Force on a Curved Current-Carrying Arc

A curved wire in the shape of an arc with radius R and central angle $$\phi$$ carries a current I an

Hard

Integral Calculation of the Magnetic Field from a Finite Straight Wire

Consider a finite straight wire of length $$L$$ carrying a steady current $$I$$. Using calculus, der

Extreme

Integrative Analysis of a Custom Magnetic Field Mapping Experiment

In a comprehensive study, a custom experimental setup was used to map the magnetic field distributio

Extreme

Interaction of Magnetic and Electric Fields in Particle Motion

A charged particle moves in a region where uniform magnetic and electric fields are oriented perpend

Extreme

Investigating the Magnetic Field Gradient in a Toroid

A toroid is constructed with a mean radius of 0.20 m, 300 turns, and carries a current of 2 A. (a) D

Hard

Investigation of Magnetic Field around a Straight Conductor

In this experiment, a student sets up a long, straight copper wire connected to a steady current sou

Medium

Investigation of Magnetic Field Interaction in a Dual-Coil System

In a dual-coil system, two identical coils are placed coaxially at a distance d from each other. Eac

Extreme

Investigation of Torque on a Wire in a Varying Magnetic Field

A laboratory experiment explores how a current-carrying wire experiences torque when subjected to a

Medium

Investigation of Torsional Stiffness Using a Twisted Wire

A wire is subjected to a torsional force generated by magnetic interactions, and its torsional stiff

Hard

Loop Geometry and Magnetic Field Distribution

Design an experiment to investigate how different loop geometries (circular vs. elliptical) affect t

Medium

Lorentz Force in a Particle Accelerator

A high-energy physics experiment report claims that the Lorentz force \(F = q*v*B\) acting on charge

Hard

Lorentz Force on a Moving Charged Particle

A charged particle with charge $$q$$ moves with velocity $$v$$ perpendicular to a uniform magnetic f

Hard

Magnetic Field Calculation Using the Biot–Savart Law

A conducting wire is bent into a semicircular shape with radius R and carries a steady current I. De

Hard

Magnetic Field from a Finite Straight Wire

A finite straight wire of length L carries a current I. A point P is located a perpendicular distanc

Extreme

Magnetic Field from a Straight Conductor

A long, straight conductor carries a constant current. Using the formula $$B = \frac{\mu_0 * I}{2\pi

Easy

Magnetic Field in a Cylindrical Conductor with Non-Uniform Current Distribution

A cylindrical conductor of radius $$R$$ carries a non-uniform current density given by $$J(r)=J_0\le

Extreme

Magnetic Field Inside a Solenoid

A solenoid is a coil of wire with a large number of turns. Consider a solenoid of length $$L$$, with

Medium

Magnetic Field Mapping of a Bar Magnet

A bar magnet is used to measure the magnetic field strength along its axial line. The following tabl

Medium

Magnetic Field Measurement around a Straight Conductor

An experimental setup is constructed to measure the magnetic field around a long straight conductor

Medium

Magnetic Field Measurement from a Straight Conductor

A researcher seeks to verify the theoretical dependence of the magnetic field on the distance from a

Easy

Magnetic Field of a Circular Current Loop via the Biot–Savart Law

The magnetic field at a point along the axis of a circular current loop can be derived using the Bio

Hard

Magnetic Field of a Composite Coil and Wire Arrangement

A composite structure consists of a circular loop of wire connected to a straight segment. (a) Der

Hard

Magnetic Field of a Straight Conductor

Consider an infinitely long straight wire carrying a constant current. Use the standard formula deri

Easy

Magnetic Field on Axis of a Circular Loop

A circular loop of radius R carries a steady current I. Using the Biot-Savart Law, derive an express

Medium

Magnetic Field Shielding using Superconductors

A superconducting ring of radius 0.1 m is used to shield a region from an applied external magnetic

Extreme

Magnetic Field Strength Inside a Solenoid with Varying Coil Turns

A research report states that the magnetic field inside a solenoid increases linearly with the numbe

Hard

Magnetic Field Variation Along the Axis of a Helical Coil

A helical coil was studied to determine how the magnetic field along its axis varies with position.

Hard

Optimization of MRI Magnetic Field Strength

An MRI machine design requires a highly uniform and strong magnetic field, generated by a solenoid.

Extreme

Particle Dynamics in Combined Electric and Magnetic Fields

An experiment studied the trajectory of a charged particle moving through a region with both electri

Extreme

Time-Varying Current and Its Magnetic Field

A long, straight wire carries a time-varying current described by $$I(t)=I_0\,\sin(\omega\,t)$$. Use

Medium

Torque on a Current-Carrying Loop

A rectangular current loop is placed in a uniform magnetic field, generating a net torque due to the

Medium

Velocity Selection in a Particle Detector

A particle detector is designed using crossed uniform electric $$E$$ and magnetic $$B$$ fields that

Extreme

Verification of the Biot–Savart Law

Design an experiment to verify the Biot–Savart Law by mapping the magnetic field produced by a small

Hard
Unit 5: Electromagnetism

Ampere's Law with Maxwell's Correction: Evaluating Magnetic Fields

A long solenoid with a turn density of 500 turns/m and carrying a current of 2 A is subjected to a r

Extreme

Analysis of Ampere's Law in a Capacitor Charging Circuit

An experiment is performed where a loop of wire is placed around a charging capacitor to measure the

Hard

Analysis of Gauss's Law using a Spherical Charge Distribution

This problem applies Gauss's Law to calculate the electric field outside a uniformly charged sphere.

Easy

Analysis of Induced Voltage Spike in an LR Circuit

In an LR circuit, opening the switch causes a rapid drop in current, resulting in a voltage spike ac

Medium

Analysis of Magnetic Flux in a Solenoid

A solenoid with 200 turns and a cross-sectional area of 0.01 m² is placed in a uniform magnetic fiel

Medium

Analysis of Magnetic Flux through a Rotating Loop

This problem investigates the magnetic flux through a rotating loop in a uniform magnetic field.

Easy

Analyzing Electric Field of a Uniformly Charged Sphere Using Gauss's Law

A researcher studies a uniformly charged sphere and measures the electric field at various distances

Medium

Application of Faraday's and Lenz's Laws in an Induction Cooktop

An induction cooktop heats a metal pot by using a coil that produces a rapidly alternating magnetic

Easy

Back EMF Analysis in an LR Circuit

A circuit consists of an inductor (L = 0.05 H) and a resistor (R = 2 Ί) in series. Initially, the ci

Easy

Combined Application of Faraday's and Lenz's Law

A bar slides on a set of conducting rails in a uniform magnetic field, inducing an EMF and a current

Medium

Damped Oscillations in an RLC Circuit

A series RLC circuit consisting of a resistor $$R$$, an inductor $$L$$, and a capacitor $$C$$ exhibi

Hard

Derivation of the Electromagnetic Wave Equation

Starting from Maxwell's equations in free space, derive the wave equations for both the electric fie

Extreme

Derivation of the Electromagnetic Wave Equation

Using Maxwell's equations in free space, derive the wave equation for the electric field $$\vec{E}(\

Extreme

Derivation of the Electromagnetic Wave Equation from Maxwell's Equations

In free space, starting from Maxwell's equations, derive the wave equation for the electric field $$

Extreme

Displacement Current in a Charging Capacitor

A researcher investigates the role of displacement current in a capacitor circuit being charged by a

Hard

Dynamic Analysis of Energy Transfer in an LC Circuit

This problem explores the oscillatory energy exchange in an LC circuit and requires both derivation

Extreme

Effect of Coil Turns on Induced EMF

A researcher varies the number of turns in a coil while keeping the rate of change of magnetic flux

Easy

Electromagnetic Induction in a Metal Detector: An Experimental Approach

A metal detector operates by generating an alternating magnetic field that induces eddy currents in

Medium

Electromagnetic Induction in a Moving Conductor

A straight conductor of length $$l$$ moves with a constant velocity $$v$$ perpendicular to a uniform

Easy

Energy Considerations in an LR Circuit Under Sudden Disconnection

In an LR circuit carrying a steady current $$I$$, the inductor stores magnetic energy which is dissi

Medium

Faraday's Law in a Non-Circular Loop

This problem explores the magnetic flux through an elliptical loop in a uniform magnetic field.

Medium

Induced EMF in a Rotating Loop

A rectangular loop of area $$A$$ rotates with constant angular velocity $$\omega$$ in a uniform magn

Medium

Induced EMF in a Time-Varying Magnetic Environment

A parallel-plate capacitor with plate area A is subjected to a time-varying magnetic field given by

Medium

Inductance in an LR Circuit

An LR circuit is constructed with an inductor of unknown inductance $$L$$ and a resistor of resistan

Medium

Induction Heating and Eddy Current Analysis

An induction heater uses electromagnetic induction to heat a metal object. The magnetic flux through

Medium

Induction Heating and Eddy Currents

A metal plate is placed above an induction coil that produces a spatially uniform alternating magnet

Hard

Induction Heating: Experimental Design and Analysis

Induction heating uses electromagnetic induction to heat conductive materials. Design an experiment

Medium

Inductor Energy Storage and Discharge

An inductor with inductance $$L$$ carries a steady current $$I$$, thereby storing magnetic energy in

Easy

Investigating Induced EMF in a Rotating Loop

A conducting loop of area $$A$$ rotates in a uniform magnetic field $$B$$ with constant angular velo

Medium

Investigation of Magnetic Flux Variation with Coil Orientation

An experiment is set up where a coil rotates at constant angular speed in a uniform magnetic field.

Hard

LC Circuit Oscillations

An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.

Easy

LR Circuit Transient Analysis

Consider an LR circuit with a resistor of resistance $$R$$ and an inductor of inductance $$L$$ conne

Medium

LR Circuit Transient Response

Consider an LR circuit comprising an inductor with inductance $$L$$ and a resistor of resistance $$R

Medium

Magnetic Flux Leakage in Practical Circuits

Magnetic flux leakage is measured on a circuit board using sensors placed along its length. The tabl

Hard

Magnetic Levitation and Electromagnetic Braking

Magnetic levitation (maglev) trains use electromagnetic induction both to levitate above the tracks

Hard

Magnetic Levitation and Induced Currents

An object with mass $$m$$ is levitated above a conducting plate due to induced eddy currents generat

Hard

Maxwell's Correction in a Charging Capacitor Circuit

In a parallel-plate capacitor being charged by a constant current, the electric field between the pl

Hard

Maxwell’s Displacement Current in a Capacitor

In a parallel-plate capacitor with plate area $$A$$ and separation $$d$$, assume that the capacitor

Hard

Maxwell's Equations and Electromagnetic Wave Propagation

Electromagnetic waves in free space are described by Maxwell's Equations. Answer the following:

Extreme

Modeling Anomalous EMF Signals in an Induction Experiment

Experimental data from an induction experiment shows that the induced EMF does not follow an ideal s

Extreme

Oscillations in an LC Circuit

An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.

Hard

Propagation of Electromagnetic Waves via Maxwell's Equations

Electromagnetic waves in a vacuum are governed by Maxwell's equations. Answer the following:

Extreme

Rotating Coil in a Uniform Magnetic Field

A rectangular coil rotates in a uniform magnetic field. The magnetic flux through the coil is given

Hard

Rotating Generator Experiment

In an experiment designed to analyze the output of a rotating generator, a coil connected to a voltm

Hard

Rotating Loop in a Uniform Magnetic Field

A rectangular loop rotates in a uniform magnetic field. An experiment recorded the induced EMF as a

Medium

Time-Varying Current Induction in a Solenoid

Consider a solenoid with n turns per unit length carrying a time-varying current given by I(t) = I₀

Medium

Time-Varying Magnetic Fields and Induced Currents

A solenoid with $$N$$ turns and cross-sectional area $$A$$ is subjected to a magnetic field that dec

Hard

Transformer Efficiency and Turn Ratios

A transformer with a primary coil of 200 turns is tested, and its secondary voltage is measured for

Medium

Transformer Efficiency Experiment

In an experiment, a transformer with a primary coil of N₁ = 1000 turns and a secondary coil of N₂ =

Easy

Transformer Efficiency Investigation

This problem examines the relationships in an ideal transformer and explores how various factors aff

Medium

Transformer Efficiency: Experimental Design and Analysis

Transformers rely on electromagnetic induction to transfer electrical energy between circuits. In th

Medium

Transient Behavior Analysis in an LR Circuit

A researcher examines the transient current behavior in an LR circuit immediately after the switch i

Medium

Transient Response in an LR Circuit

An LR circuit consists of a resistor $$R = 10$$ Ί and an inductor $$L = 2$$ H. A step voltage of 20

Medium

Variable Capacitance in an LC Circuit: Resonant Frequency Analysis

In an LC circuit, suppose the capacitance varies with time as C(t) = C₀*(1 + α*t), where α is a smal

Medium

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Tips from Former AP Students

FAQWe thought you might have some questions...
Where can I find practice free response questions for the AP Physics C: Electricity and Magnetism exam?
The free response section of each AP exam varies slightly, so you’ll definitely want to practice that before stepping into that exam room. Here are some free places to find practice FRQs :
  • Of course, make sure to run through College Board's past FRQ questions!
  • Once you’re done with those go through all the questions in the AP Physics C: Electricity and MagnetismFree Response Room. You can answer the question and have it grade you against the rubric so you know exactly where to improve.
  • Reddit it also a great place to find AP free response questions that other students may have access to.
How do I practice for AP AP Physics C: Electricity and Magnetism Exam FRQs?
Once you’re done reviewing your study guides, find and bookmark all the free response questions you can find. The question above has some good places to look! while you’re going through them, simulate exam conditions by setting a timer that matches the time allowed on the actual exam. Time management is going to help you answer the FRQs on the real exam concisely when you’re in that time crunch.
What are some tips for AP Physics C: Electricity and Magnetism free response questions?
Before you start writing out your response, take a few minutes to outline the key points you want to make sure to touch on. This may seem like a waste of time, but it’s very helpful in making sure your response effectively addresses all the parts of the question. Once you do your practice free response questions, compare them to scoring guidelines and sample responses to identify areas for improvement. When you do the free response practice on the AP Physics C: Electricity and Magnetism Free Response Room, there’s an option to let it grade your response against the rubric and tell you exactly what you need to study more.
How do I answer AP Physics C: Electricity and Magnetism free-response questions?
Answering AP Physics C: Electricity and Magnetism free response questions the right way is all about practice! As you go through the AP AP Physics C: Electricity and Magnetism Free Response Room, treat it like a real exam and approach it this way so you stay calm during the actual exam. When you first see the question, take some time to process exactly what it’s asking. Make sure to also read through all the sub-parts in the question and re-read the main prompt, making sure to circle and underline any key information. This will help you allocate your time properly and also make sure you are hitting all the parts of the question. Before you answer each question, note down the key points you want to hit and evidence you want to use (where applicable). Once you have the skeleton of your response, writing it out will be quick, plus you won’t make any silly mistake in a rush and forget something important.