AP Physics C: Electricity and Magnetism FRQ Room
Ace the free response questions on your AP Physics C: Electricity and Magnetism exam with practice FRQs graded by Kai. Choose your subject below.
Knowt can make mistakes. Consider checking important information.
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.
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
Analyzing Electric Field Inside a Uniformly Charged Sphere
Design an experiment to measure the electric field at various points inside a uniformly charged insu
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
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
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
Capacitor Charging in an RC Circuit
A capacitor with capacitance $$C$$ is charged through a resistor $$R$$ by a constant voltage source
Capacitor with Dielectric Insertion
This problem examines how the capacitance and stored energy of a parallel plate capacitor change whe
Charge Conservation and Electrostatic Interactions
Charge conservation and electrostatic interactions are fundamental concepts in electromagnetism. Dis
Comparative Analysis of Conductors and Insulators
An experiment compares the charge retention in a conductor versus an insulator when both are initial
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)
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
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
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
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
Electric Field and Potential Gradient
This question deals with the relationship between electric potential and the electric field in the v
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
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:
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
Electric Field from a Cylindrical Charge Distribution
An infinitely long cylindrical rod of radius $$R = 0.05 \; m$$ carries a uniform volume charge densi
Electric Field from a Uniformly Charged Rod
A researcher is studying the electric field produced by a thin rod of length $$L$$, uniformly charge
Electric Field from an Extended Linear Charge Distribution
A thin rod of length $$L = 0.50 \; m$$ has a uniform linear charge density $$\lambda = 2.0*10^{-8} \
Electric Field from an Infinite Plane of Charge
A large, flat surface carries a uniform surface charge density of $$\sigma = 3.0*10^{-6} \; C/m^2$$.
Electric Field Inside a Uniformly Charged Sphere
A nonconducting sphere of radius $$R = 0.20 \; m$$ carries a uniformly distributed charge $$Q = +5.0
Electric Field of a Conducting Sphere
A conducting sphere of radius R is uniformly charged with total charge Q. Answer the following quest
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
Electric Flux and Gauss' Law in Different Geometries
Students conduct a computer simulation of electric flux through various closed surfaces, including a
Electric Force Between Point Charges
This question addresses the calculation of the electrostatic force between two point charges using C
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
Electric Potential Energy in a System of Charges
Consider a system of point charges. Explore the concept of electric potential energy within this sys
Electrostatic Force Variation with Distance
An experiment is conducted to verify Coulomb's law by measuring the force between two point charges
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
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
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
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
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
Gauss' Law for a Non-Uniform Spherical Charge Distribution
Consider a sphere of radius R with a radial dependent charge density given by $$\rho(r) = \rho_0*(r/
Gaussâs Law in a Uniformly Charged Sphere
A nonâconducting sphere of radius R = 0.5 m carries a uniformly distributed charge Q = 1.0Ă10âťâś C. U
Integrating Charge Density to Determine Total Charge in a Spherical Volume
In an experiment, the volume charge density inside a sphere is modeled by Ď(r) = Ďâ e^(-r), where Ďâ
Integration to Determine Electric Potential along a Line
A uniformly charged rod creates an electric potential along its axis. Determine this potential using
Investigating Electric Fields in Conductors vs. Insulators
Design an experiment to compare the electric field distribution around a metallic (conductor) sphere
Investigating the Relationship between Electric Flux and Surface Geometry
A simulation is designed to explore how electric flux through a surface depends on the geometry of t
Measuring Electric Field Lines using Near-field Probes
In this experiment, a set of movable near-field probes is used to measure the spatial variation of t
Measuring the Polarization Effects in an Insulating Material
An experiment is set up to study polarization in an insulating material. The material is placed in a
Multi-Charge Interaction Analysis
Three point charges are located at the vertices of an equilateral triangle with side length $$0.10 \
Non-Uniform Charge Distribution in a Sphere
Consider a sphere of radius $$R$$ in which the volume charge density varies with radius as $$\rho(r)
Optimization of Non-uniform Charge Distribution
A researcher aims to optimize the electric field at a point P on the y-axis (distance $$d$$ from the
Point Charge Interaction Experiment
Two point charges are fixed in space, and an experiment is carried out to measure the force experien
Point Charge Interactions and Coulomb's Law
Two point charges are placed along the x-axis in a vacuum. Let $$q_1 = +1.602*10^{-19} \; C$$ be loc
Point Charge Potential Calculation
Consider a point charge of $$Q = 4.00 \; \mu C$$. (a) Derive the expression for the electric potent
Point Charges and Coulomb's Law Analysis
Consider two point charges placed along a horizontal line. Use Coulomb's law to analyze the interact
Transient Behavior in an RC Circuit
A researcher studies the transient discharge of a capacitor in an RC circuit.
Uniform Electric Field in a Finite Charged Plate Experiment
An experiment is designed to verify the existence of a uniform electric field produced by a large, f
Work Done by a Uniform Electric Field
This problem examines the work done on a charged particle as it moves in a uniform electric field an
Work Done by Electric Fields in a Particle Accelerator
In designing a particle accelerator, a researcher wants to determine the work done by a constant ele
Work Done in a Non-Uniform Electric Field
This question requires you to compute the work done on a charge moving through a spatially varying (
Work Done Moving a Charge in a Point Charge Field
A charge q is moved in the electric field of a point charge Q from a distance râ to râ. Using calcul
Analysis of Capacitors in Series and Parallel
A circuit contains three capacitors arranged such that capacitors $$C_1$$ and $$C_2$$ are connected
Analyzing Charge Distribution on a Composite Conductor
A researcher explores a composite conductor comprising regions with different curvatures and materia
Analyzing Dielectric Constant Influence on Capacitance
When a dielectric is inserted into a capacitor, its capacitance increases. Consider the following ta
Capacitive Sensor Response
A capacitive sensor is designed to measure tiny changes in the distance between its parallel plates.
Capacitor as a Pressure Sensor
A parallel plate capacitor is used as a pressure sensor. When pressure is applied, one of the plates
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 \
Capacitor with Layered Dielectrics
A parallel plate capacitor is constructed using two different dielectric layers arranged in series.
Comparative Analysis of Capacitor Types in High Frequency Circuits
A study was performed to compare different types of capacitorsâceramic, electrolytic, film, and tant
Composite Dielectric Capacitor Analysis
A capacitor is built with two different dielectric layers in series. The first layer has thickness \
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
Deriving the Zero Electric Field Inside a Conductor
Use Gaussâ law and the boundary conditions at the surface of a conductor to prove that the electric
Designing a Faraday Cage for Sensitive Instrumentation
A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo
Determining Dielectric Constant Experimentally
In an experiment, a set of identical parallel plate capacitors is assembled with different dielectri
Dielectric Strength and Material Breakdown Analysis
A capacitor with a dielectric material of thickness \(d\) is subject to an electric field. The diele
Dynamic Parallel Plate Capacitor
A parallel plate capacitor is charged to a constant charge $$Q$$ but has a plate separation that inc
Effect of Dielectrics on Capacitance
A capacitor initially in vacuum with capacitance $$C_0$$ has a dielectric material with dielectric c
Effect of Dielectrics on Capacitance: A Comparative Study
A researcher investigates the effect of different dielectric materials on the capacitance of a paral
Electric Shielding Efficiency in a Laboratory Setting
A researcher tests the effectiveness of different conductive materials as electric shields. The shie
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
Experimental Analysis of Dielectric Breakdown
A researcher investigates the dielectric strength of several insulating materials. The experiment in
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
FRQ 7: Capacitor Discharge with a Time-Dependent Resistor
In an experimental circuit, a capacitor of capacitance $$C$$ is discharged through a resistor whose
FRQ 10: Charge Distribution on Curved Conductors
An experiment is undertaken to measure the electric field strength at various points on an irregular
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
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
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
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
Investigation of a Variable Capacitor
A variable capacitor is tested by adjusting its knob position, and the corresponding capacitance is
Investigation of Dielectric Breakdown Voltage
A study was conducted to investigate the breakdown voltage of dielectric materials. The breakdown vo
Modeling Electric Field Interactions Between Two Conductors
When two conductors are placed in close proximity, their electric fields interact. Design an experim
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
Parallel Plate Capacitor with Gradually Varying Dielectric
Consider a parallel plate capacitor with plate area $$A$$ and separation $$d$$, where the dielectric
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
RC Circuit Transient Analysis
A capacitor with capacitance $$C$$ is connected in series with a resistor $$R$$ and a constant volta
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
RC Circuit: Charging and Discharging Capacitor Analysis
A capacitor is charged through a resistor from a constant voltage source and then allowed to dischar
Surface Charge Redistribution on Irregularly Shaped Conductors
An irregularly shaped conductor has varying curvature along its surface, leading to a non-uniform su
Time-Dependent Dielectric Breakdown Analysis
A dielectric material of thickness $$d$$ has a breakdown electric field strength $$E_{break}$$. In r
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
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
Analysis of Power Supply Stability
Examine a power supply circuit where the output voltage is affected by varying load conditions. Use
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
Analyzing the Effect of Temperature on Resistivity in a Circuit
A conductor's resistance varies with temperature according to the formula $$R = R_0 (1+ \alpha (T-T_
Application of Kirchhoffâs Current Law at a Complex Node
At a junction with multiple branches, apply Kirchhoffâs Current Law (KCL) and explore the implicatio
Applying Kirchhoff's Current Law in a Multi-Branch Network
A complex circuit node has three branches with currents measured experimentally. Use Kirchhoff's Cur
Battery EMF and Terminal Voltage Analysis
A non-ideal battery has an electromotive force (EMF) of 9 V and an internal resistance of 1 Ί. It is
Battery EMF with Time-Varying Load
A battery with an electromotive force (EMF) of 9 V and an internal resistance of 0.5 Ί is connected
Capacitors in Series: Voltage Division Analysis
A series circuit contains three capacitors with values $$C_{1}=2\,\mu F$$, $$C_{2}=3\,\mu F$$, and $
Characterizing a Non-Ideal Battery from Experimental Data
A researcher collects data on a batteryâs performance by measuring its terminal voltage under variou
Complex Circuit Analysis using Kirchhoffâs Laws
Consider a circuit with three nodes where one resistor has a time-varying resistance given by $$R(t)
Effect of Temperature on Resistor Resistance
A resistor's resistance varies with temperature as $$R(T)=R_0*(1+\alpha*(T-T_0))$$, where $$R_0=50\;
Energy Storage in Capacitors and Inductors
Using calculus, derive the expressions for the energy stored in (a) a capacitor with capacitance C c
Evaluating Measurement Errors in Circuit Instruments
Measurement errors in electrical instruments can propagate through calculations. Evaluate the error
Evaluating Power and Efficiency in an Electric Motor Circuit
This question assesses your understanding of power calculations in electrical circuits and your abil
Frequency Dependence of Capacitive Reactance
Investigate how the capacitive reactance in an AC circuit depends on frequency, and use calculus to
FRQ 1: Basic Circuit Calculations Using Ohm's Law
A simple circuit consists of a battery and a single resistor. The battery provides a voltage of $$12
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 $$8\,\Omega$$.
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: $
Ideal Versus Non-Ideal Circuit Component Analysis
Theoretical models using ideal circuit components often predict behavior that deviates from experime
Impact of Temperature on Resistance
Resistance in a conductor can change with temperature. Investigate this variation and its implicatio
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.
Investigating Temperature-Dependent Resistance of a Thermistor
This question explores how the resistance of a thermistor varies with temperature, requiring both ma
Kirchhoffâs Laws in Multi-loop Circuits
Design a circuit that consists of two loops which share a common resistor. The circuit includes two
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
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
Measuring Power Dissipation in Resistive Circuits
This question examines the derivation of power relationships in resistive circuits and requires you
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 $$0.8
Multi-Loop Circuit Analysis using Kirchhoff's Laws
A circuit consists of two loops that share a common resistor. A student claims that by applying Kirc
Non-Ideal Battery EMF Measurement with Internal Resistance Error
A researcher attempts to measure the electromotive force (EMF) of a battery by connecting a voltmete
Parallel Circuit Current Distribution Error Analysis
A student conducts an experiment on a parallel resistor network powered by a constant voltage source
Power Consumption in a Resistor Under Time-Varying Voltage
A student conducts an experiment on a resistor and claims that the power consumption follows the for
Power Dissipation and Energy in a Resistive Circuit
A resistive circuit is powered by a constant current source. Examine the energy transfer in the resi
Power Dissipation and Non-Ideal Battery Analysis
Examine a circuit where a non-ideal battery with an electromotive force (EMF) of $$\mathcal{E} = 12\
RC Circuit Transient Analysis
An RC circuit is constructed with a resistor \(R = 2.0\,\Omega\) and a capacitor \(C = 5.0 \times 10
Resonance and Quality Factor in an LCR Circuit
A researcher examines an LCR series circuit comprising an inductor $$L=0.1\,H$$, a capacitor $$C=100
Resonance in an RLC Circuit
Consider a series RLC circuit with $$R = 15\,\Omega$$, $$L = 0.2\,H$$, and $$C = 50\,\mu F$$ powered
Series Circuit Analysis with Calculus Application
A researcher is investigating a series circuit in which three resistors (with initial values $$R_{1}
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}+
Temperature Effects on Conductor Resistance and Circuit Current
A researcher studies how temperature affects the resistance of a conductor. The resistance is given
Temperature Effects on Resistance
A researcher investigates how temperature affects the resistance of a thermistor. The experiment mea
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
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
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
Analysis of Forced Oscillations in a Magnetic Pendulum
A novel experiment involves a magnetic pendulum oscillating within a time-varying external magnetic
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
Application of the Right-Hand Rule
A straight, horizontal wire carries a current of $$5 * A$$ from left to right. Using the right-hand
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
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 $$J(x) = J_0(1 + 0
Calculus in Magnetic Induction: Time-Varying Current Effects
A solenoid with 400 turns over a length of 0.8 m is driven by a time-varying current expressed as $$
Comparison of Magnetic Fields from Different Geometries
A researcher compares the magnetic fields produced by different geometries â a straight wire, a circ
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.
Derivation of Ampèreâs Law via Loop Integration
Consider a long straight wire carrying a constant current I. Derive Ampèreâs Law for a circular loop
Designing a Magnetic Crane with Controlled Current
A magnetic crane used in industrial lifting uses large current-carrying conductors to generate a str
Designing a Magnetic Levitation System
An engineer designs a magnetic levitation system where a current-carrying wire is used to levitate a
Designing an Electromagnetic Levitation System
An engineering team is developing an electromagnetic levitation system for a high-speed train. The c
Determining Torsional Stiffness from Angular Deflection Data
A metal wire is twisted by applying varying torques. The resulting angular deflection (in radians) w
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
Determining Torsional Stiffness Using Magnetic Torque
A current-carrying wire is twisted by an external magnetic field, generating a measurable torque. (
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
Effect of Wire Orientation on Lorentz Force
A current-carrying wire oriented at different angles relative to a uniform magnetic field experience
Evaluating Magnetic Field Distribution in a Halved Solenoid
A long solenoid is physically divided into two equal halves. (a) Using integration, derive express
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
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
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
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
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
Force Between Two Parallel Current-Carrying Wires
A study claims that the attractive force per unit length between two parallel wires carrying current
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
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
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
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
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
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
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
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
Investigation of Torsional Stiffness Using a Twisted Wire
A wire is subjected to a torsional force generated by magnetic interactions, and its torsional stiff
Loop Geometry and Magnetic Field Distribution
Design an experiment to investigate how different loop geometries (circular vs. elliptical) affect t
Lorentz Force in a Particle Accelerator
A high-energy physics experiment report claims that the Lorentz force \(F = q*v*B\) acting on charge
Lorentz Force on a Moving Charged Particle
A charged particle with charge $$q$$ moves with velocity $$v$$ perpendicular to a uniform magnetic f
Magnetic Field Calculation Using the BiotâSavart Law
A conducting wire is bent into a semicircular shape with radius R and carries a steady current I. De
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
Magnetic Field from a Straight Conductor
A long, straight conductor carries a constant current. Using the formula $$B = \frac{\mu_0 * I}{2\pi
Magnetic Field in a Cylindrical Conductor with Non-Uniform Current Distribution
A cylindrical conductor of radius $$R$$ carries a non-uniform current density given by $$J(r)=J_0\le
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
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
Magnetic Field Measurement around a Straight Conductor
An experimental setup is constructed to measure the magnetic field around a long straight conductor
Magnetic Field Measurement from a Straight Conductor
A researcher seeks to verify the theoretical dependence of the magnetic field on the distance from a
Magnetic Field of a Circular Current Loop via the BiotâSavart Law
The magnetic field at a point along the axis of a circular current loop can be derived using the Bio
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
Magnetic Field of a Straight Conductor
Consider an infinitely long straight wire carrying a constant current. Use the standard formula deri
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
Magnetic Field Shielding using Superconductors
A superconducting ring of radius 0.1 m is used to shield a region from an applied external magnetic
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
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.
Optimization of MRI Magnetic Field Strength
An MRI machine design requires a highly uniform and strong magnetic field, generated by a solenoid.
Particle Dynamics in Combined Electric and Magnetic Fields
An experiment studied the trajectory of a charged particle moving through a region with both electri
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
Torque on a Current-Carrying Loop
A rectangular current loop is placed in a uniform magnetic field, generating a net torque due to the
Velocity Selection in a Particle Detector
A particle detector is designed using crossed uniform electric $$E$$ and magnetic $$B$$ fields that
Verification of the BiotâSavart Law
Design an experiment to verify the BiotâSavart Law by mapping the magnetic field produced by a small
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
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
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.
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
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
Analysis of Magnetic Flux through a Rotating Loop
This problem investigates the magnetic flux through a rotating loop in a uniform magnetic field.
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
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
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
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
Damped Oscillations in an RLC Circuit
A series RLC circuit consisting of a resistor $$R$$, an inductor $$L$$, and a capacitor $$C$$ exhibi
Derivation of the Electromagnetic Wave Equation
Starting from Maxwell's equations in free space, derive the wave equations for both the electric fie
Derivation of the Electromagnetic Wave Equation
Using Maxwell's equations in free space, derive the wave equation for the electric field $$\vec{E}(\
Derivation of the Electromagnetic Wave Equation from Maxwell's Equations
In free space, starting from Maxwell's equations, derive the wave equation for the electric field $$
Displacement Current in a Charging Capacitor
A researcher investigates the role of displacement current in a capacitor circuit being charged by a
Dynamic Analysis of Energy Transfer in an LC Circuit
This problem explores the oscillatory energy exchange in an LC circuit and requires both derivation
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
Electromagnetic Induction in a Metal Detector: An Experimental Approach
A metal detector operates by generating an alternating magnetic field that induces eddy currents in
Electromagnetic Induction in a Moving Conductor
A straight conductor of length $$l$$ moves with a constant velocity $$v$$ perpendicular to a uniform
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
Faraday's Law in a Non-Circular Loop
This problem explores the magnetic flux through an elliptical loop in a uniform magnetic field.
Induced EMF in a Rotating Loop
A rectangular loop of area $$A$$ rotates with constant angular velocity $$\omega$$ in a uniform magn
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
Inductance in an LR Circuit
An LR circuit is constructed with an inductor of unknown inductance $$L$$ and a resistor of resistan
Induction Heating and Eddy Current Analysis
An induction heater uses electromagnetic induction to heat a metal object. The magnetic flux through
Induction Heating and Eddy Currents
A metal plate is placed above an induction coil that produces a spatially uniform alternating magnet
Induction Heating: Experimental Design and Analysis
Induction heating uses electromagnetic induction to heat conductive materials. Design an experiment
Inductor Energy Storage and Discharge
An inductor with inductance $$L$$ carries a steady current $$I$$, thereby storing magnetic energy in
Investigating Induced EMF in a Rotating Loop
A conducting loop of area $$A$$ rotates in a uniform magnetic field $$B$$ with constant angular velo
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.
LC Circuit Oscillations
An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.
LR Circuit Transient Analysis
Consider an LR circuit with a resistor of resistance $$R$$ and an inductor of inductance $$L$$ conne
LR Circuit Transient Response
Consider an LR circuit comprising an inductor with inductance $$L$$ and a resistor of resistance $$R
Magnetic Flux Leakage in Practical Circuits
Magnetic flux leakage is measured on a circuit board using sensors placed along its length. The tabl
Magnetic Levitation and Electromagnetic Braking
Magnetic levitation (maglev) trains use electromagnetic induction both to levitate above the tracks
Magnetic Levitation and Induced Currents
An object with mass $$m$$ is levitated above a conducting plate due to induced eddy currents generat
Maxwell's Correction in a Charging Capacitor Circuit
In a parallel-plate capacitor being charged by a constant current, the electric field between the pl
Maxwellâs Displacement Current in a Capacitor
In a parallel-plate capacitor with plate area $$A$$ and separation $$d$$, assume that the capacitor
Maxwell's Equations and Electromagnetic Wave Propagation
Electromagnetic waves in free space are described by Maxwell's Equations. Answer the following:
Modeling Anomalous EMF Signals in an Induction Experiment
Experimental data from an induction experiment shows that the induced EMF does not follow an ideal s
Oscillations in an LC Circuit
An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.
Propagation of Electromagnetic Waves via Maxwell's Equations
Electromagnetic waves in a vacuum are governed by Maxwell's equations. Answer the following:
Rotating Coil in a Uniform Magnetic Field
A rectangular coil rotates in a uniform magnetic field. The magnetic flux through the coil is given
Rotating Generator Experiment
In an experiment designed to analyze the output of a rotating generator, a coil connected to a voltm
Rotating Loop in a Uniform Magnetic Field
A rectangular loop rotates in a uniform magnetic field. An experiment recorded the induced EMF as a
Time-Varying Current Induction in a Solenoid
Consider a solenoid with n turns per unit length carrying a time-varying current given by I(t) = Iâ
Time-Varying Magnetic Fields and Induced Currents
A solenoid with $$N$$ turns and cross-sectional area $$A$$ is subjected to a magnetic field that dec
Transformer Efficiency and Turn Ratios
A transformer with a primary coil of 200 turns is tested, and its secondary voltage is measured for
Transformer Efficiency Experiment
In an experiment, a transformer with a primary coil of Nâ = 1000 turns and a secondary coil of Nâ =
Transformer Efficiency Investigation
This problem examines the relationships in an ideal transformer and explores how various factors aff
Transformer Efficiency: Experimental Design and Analysis
Transformers rely on electromagnetic induction to transfer electrical energy between circuits. In th
Transient Behavior Analysis in an LR Circuit
A researcher examines the transient current behavior in an LR circuit immediately after the switch i
Transient Response in an LR Circuit
An LR circuit consists of a resistor $$R = 10$$ Ί and an inductor $$L = 2$$ H. A step voltage of 20
Variable Capacitance in an LC Circuit: Resonant Frequency Analysis
In an LC circuit, suppose the capacitance varies with time as C(t) = Câ*(1 + Îą*t), where Îą is a smal
Trusted by millions
Everyone is relying on Knowt, and we never let them down.
Need to review before working on AP Physics C: Electricity and Magnetism FRQs?
We have over 5 million resources across various exams, and subjects to refer to at any point.
Explore Top AP Physics C: Electricity and Magnetism Flashcards
Flashcards (123)Explore Top AP Physics C: Electricity and Magnetism Notes
Note Browse top AP materials
Weâve found the best flashcards & notes on Knowt.
Explore top AP flashcards
Explore top AP notes
Tips from Former AP Students
- Of course, make sure to run through College Board's past FRQ questions!
- Once youâre 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.