AP Physics 2: Algebra-Based FRQ Room

Airflow Over a Wing

An airplane wing has a surface area of 16 m². The pressure difference between the bottom and the top

Analyzing Pressure in a U-Tube Manometer

A U-tube manometer utilizes two different fluids (water and mercury) to measure pressure differences

Bernoulli's Equation and Pressure Variation in a Constricted Pipe

A pump forces water (with density $$1000\;kg/m^{3}$$) through a pipe that gradually narrows. At poin

Bernoulli’s Equation in a Constricted Pipe

A pump forces water through a horizontal pipe that gradually constricts. At point 1 (where the pipe

Bernoulli's Equation with Elevation Change

Water flows from a pump at point 1 where the speed is 1 m/s (elevation 0). It then flows to point 2,

Bernoulli's Equation with Incorrect Height Reference

A student constructs an experiment using a pipe system with both horizontal and vertical segments to

Bernoulli’s Principle and Air Flow Over an Airfoil

An airfoil (wing cross-section) diagram shows streamlines of air with different velocities above and

Bernoulli's Principle and Aircraft Lift

Air flows over the upper and lower surfaces of an airplane wing. In a certain section along the wing

Bernoulli's Principle in a Constricted Pipe

A pump forces water through a horizontal pipe that narrows gradually. At point 1 the cross-sectional

Buoyancy and Stability of a Floating Vessel

A small vessel is floating in water and is depicted in the provided diagram.

Buoyancy Experiment with Incorrect Variable Substitution

A student designs an experiment to determine the fraction of an object's volume that is submerged wh

Buoyancy in Multi-fluid Systems

This problem examines buoyancy when an object is in contact with two immiscible fluids, requiring de

Buoyant Stability and Metacentric Height in Floating Bodies

A floating vessel is designed with specific dimensions to ensure stability. A diagram of the vessel’

Capillary Action: Investigating the Rise of Liquid in Narrow Tubes

Design an experiment to measure the capillary rise of a liquid in tubes of various diameters. Your e

Column Pressure Analysis

A series of experiments is conducted to analyze the pressure exerted by vertical cement columns on t

Comparative Study of Fluids Using a U-Tube Manometer

In a laboratory, students use a U-tube manometer to compare the densities of two unknown fluids. The

Continuity and Bernoulli in a River Channel

A river flows from a wide channel into a narrow section. In the wide channel, the cross-sectional ar

Continuity Equation and Variable Pipe Flow

A horizontal pipe carrying a fluid branches into two tubes of different diameters. Analyze the situa

Density and Pressure of a Cement Column

A vertical cement column with a base area of $$0.5 \cdot m^2$$ and a height of $$2 \cdot m$$ is cons

Density Determination and Fluid Identification

This problem focuses on calculating density and using that result to discuss buoyancy. Answer the fo

Density Determination Experiment

A student performs an experiment to determine the density of three different liquids by measuring sm

Density Determination Using a Hydrometer Experiment

In an experiment to determine the density of various liquids, a hydrometer is used. The operating pr

Design Considerations for Submerged Structures

An engineer is designing a submerged structure that must resist external fluid pressure. (a) Derive

Designing a Water Fountain: Pressure and Flow

A landscape architect is designing a water fountain and needs the water jet to reach a maximum heigh

Determining Buoyant Force on a Partially Submerged Object

A physics student examines the buoyant force experienced by an object when it is partially submerged

Diver's Pressure: Hydrostatic and Atmospheric Contributions

A diver descends to a depth of 30 m in seawater with a density of 1025 kg/m³. The atmospheric pressu

Effect of Elevation Changes on Fluid Flow Speed and Pressure

A researcher investigates how a vertical drop in a pipeline affects fluid kinetic energy and pressur

Energy Conversion in Hydraulic Systems

Hydraulic systems utilize fluid flow to convert energy and perform work. As fluid flows, energy is t

Examining Temperature Effects on Density and Pressure

A fluid contained in a sealed vessel is heated from $$20^\circ C$$ to $$80^\circ C$$. At $$20^\circ

Flow in an Open Channel: Continuity and Energy Considerations

Water flows in an open channel that narrows from a width of 4.0 m to 2.0 m. In the wider section, th

Flow Rate Conundrum in a Diverging-Nozzle Experiment

A diverging-converging nozzle experiment reports that increasing the nozzle diameter leads to a decr

Flow Rate in a Constricted Pipe

Consider a circular pipe carrying water. The pipe has a radius of 2 cm and the water flows at a spee

Flow Rate in a Non-uniform Pipe

A researcher examines fluid flow through a non-uniform circular pipe where the fluid is assumed to b

Fluid Depth Pressure Graph Analysis

A pressure sensor is used to measure the pressure at different depths in a water tank. The following

Fluid Exit Velocity: An Orifice Flow Experiment

A group of students conducts an experiment to measure the speed of water exiting a small orifice at

Fluid Flow in an Open-Channel System: Integration of Concepts

A researcher conducts a comprehensive investigation of fluid flow in an open-channel system (e.g., a

Fluid Flow in Industrial Piping Systems

In an industrial setup, water is transported through pipes with varying diameters. Measurements for

Force Analysis on a Dam Structure Using Fluid Pressure

A dam holds back a reservoir of water with a depth of 20 m. The vertical face of the dam has a width

Hydraulic Press and Force Amplification

A hydraulic press consists of two pistons connected by an incompressible fluid. The larger piston ha

Hydrostatic Pressure and Exit Velocity from a Reservoir

A large dam reservoir holds water with a density of 1000 kg/m³. Atmospheric pressure is $$101325\;Pa

Hydrostatic Pressure in an Open Tank

A researcher investigates hydrostatic pressure within an open water tank. The study aims to measure

Hydrostatic Pressure in Fluid Tanks

A tank is filled with water (density = $$1000 \cdot kg/m^3$$). The gauge pressure in the tank is mea

Hydrostatic Pressure Miscalculation Experiment

A student sets up an experiment to measure the pressure at the bottom of a water tank. The student f

Industrial Fluid Density and Pressure Calculation

A researcher in an industrial laboratory is studying fluid properties for engineering applications.

Interpretation and Analysis of a Fluid Flow Schematic

A schematic diagram is provided that represents fluid flow in a horizontal pipe system. The diagram

Interpreting a Diagram of Fluid Density Distribution

A container holds multiple immiscible fluids layered according to density. The provided diagram show

Investigating Air Pressure Changes with Altitude

A researcher measures atmospheric pressure at different altitudes to study its variation with elevat

Investigating Pressure Differences in Fluid Circuits

A U-shaped tube contains a fluid with a density of 1200 kg/m³. A small height difference between the

Investigating the Effect of Temperature on Fluid Density

Temperature changes can affect the density of a fluid. a) Explain qualitatively how increasing tem

Manometer Pressure Measurements

An experiment uses a U-tube manometer filled with water to measure pressure differences in a fluid s

Measurement of Flow Rate in a Venturi Meter

A venturi meter is installed in a pipeline to measure flow rate by producing a pressure drop at the

Measuring Hydrostatic Pressure in an Underwater Environment

An oceanographer sets up an experiment to measure the hydrostatic pressure as a function of depth in

Mercury Barometer Atmospheric Pressure Measurement

An experiment employs a mercury barometer to measure atmospheric pressure. The claim is that the hei

Open Channel Pressure Measurement

In an open channel flow experiment, gauge pressures were measured at different depths below the free

Pipe Flow Continuity

An experiment examines fluid flow through a pipe with a constricted section. The following table sho

Pressure Distribution in an Accelerating Container

A rectangular container filled with water (density $$1000\;kg/m^3$$) is accelerated horizontally at

Pressure Exerted by a Fluid Column

A concrete column has a height of 3 m, a base area of 1 m², and a density of 2400 kg/m³. Answer the

Pressure in a Fluid with Depth-Dependent Density

In a non-uniform fluid, the density varies with depth according to $$\rho(y) = \rho_0 + \alpha y$$,

Pressure Variation in a Fluid Column

A tall building has a water tank located on its roof, 50 m above ground level. (a) Calculate the hyd

Solar-Powered Water Pump Analysis in a Remote Village

In a remote village, a solar-powered water pump extracts water from a well 20 m deep. The pump must

Solid Column Pressure Calculation

A vertical column made of cement is used in a structural experiment. The column has a uniform cross-

Temperature Effects on Fluid Density and Pressure

A particular fluid has a density of 950 kg/m³ at 20°C and its density decreases by 0.2% for every 1°

Analysis of Atmospheric Pressure and Gas Density

Explain why the high pressure generated by confined gas does not cause the container lid to pop off,

Analysis of Isothermal Process Cycle Using a P–V Diagram

Isothermal processes occur at constant temperature, and the work done can be determined from a P–V d

Analyzing Deviations from the Ideal Gas Law

A researcher measures the pressure of a gas at various volumes and observes deviations from the Idea

Comparative Analysis of Heat Engine Cycles

Two heat engines, Engine A and Engine B, operate under different conditions. Their heat inputs and o

Comparing Real and Ideal Gas Behavior

Discuss the limitations of the Ideal Gas Law and explain the necessary corrections for real gases us

Derivation of the Root Mean Square Velocity

Starting from the average kinetic energy equation $$\frac{1}{2} m(v^2)_{avg} = \frac{3}{2} k_B T$$,

Designing a Convection Experiment

Develop an experimental proposal to investigate how fluid temperature affects the rate of convective

Differentiating Heat Transfer Modes: Convection vs. Conduction

An experiment compares the rate of heat transfer in two different setups: one using a fluid medium (

Effect of Molar Mass on Gas Velocity

The relation $$v_{rms} = \sqrt{\frac{3 * k_{B} * T}{m}}$$ indicates that the molar mass of gas molec

Effect of Molecular Mass on RMS Velocity

The root-mean-square velocity of gas molecules is given by $$v_{rms} = \sqrt{\frac{3k_BT}{m}}$$. (a)

Energy Conversion in a Steam Engine

A steam engine operates with an efficiency of 30% and absorbs 2000 J of heat per cycle. (a) Calcula

Entropy Change in Thermodynamic Processes

Entropy is a measure of disorder within a system. (a) Define entropy in the context of thermodynamic

Entropy Changes in Thermodynamic Processes

Consider an ideal gas that undergoes an isothermal expansion from an initial volume $$V_1$$ to a fin

Evaluating the Role of Pressure Differences in Atmospheric Applications

A high-altitude weather balloon collects data on atmospheric pressure as it ascends. The recorded da

Force Exerted by a Confined Gas

A cylindrical container is used to confine an ideal gas. The following parameters are provided in th

Force on Container Lid from Confined Gas

A cylindrical container has a radius of 15 cm and a height of 30 cm. It contains 0.6 moles of an ide

Heat Engine Efficiency

A heat engine draws $$800\;J$$ of heat from a high-temperature source and rejects $$450\;J$$ of heat

Heat Engine Efficiency Analysis

A heat engine operates by drawing heat from a high-temperature source and rejecting part of it as ex

Heat Engine Performance Measurements

A heat engine operates in cycles, drawing 800 J of heat from its high-temperature reservoir and reje

Heat Transfer by Conduction

For a metal rod, the rate of heat transfer by conduction is described by $$\frac{Q}{\Delta t}=\frac{

Heating a Gas: Conduction vs. Convection

Heat can be transferred via different mechanisms. In the context of a gas being heated, consider the

Identifying Thermodynamic Processes

A series of experiments with a gas record measurements of pressure, volume, and temperature. The dat

Influence of Molecular Mass on Gas Pressure and Speed

Two gases are each confined in identical rigid containers. Both contain the same number of molecules

Interpreting a Maxwell-Boltzmann Speed Distribution Graph

Analyze the Maxwell-Boltzmann speed distribution graph provided and answer the following.

Investigating the Role of Atmospheric Pressure in Sealed Container Systems

The net force on a container’s lid results from the difference between the internal gas pressure and

Investigation of Convection Currents in Fluids

A transparent tank filled with water is heated from below. A dye is introduced to visualize the resu

Kinetic Energy and Temperature Relationship

A sample of an ideal gas is described by the kinetic theory: $$v_{rms} = \sqrt{\frac{3 * k_{B} * T}{

Radiative Heat Transfer Experiment Error

In an experiment designed to quantify radiative heat transfer, a student sets up a hot plate surroun

Reversibility and Work in Thermodynamic Cycles

A reversible thermodynamic cycle is performed, and a P–V diagram of the cycle is recorded. Use the d

Specific Heat Capacity Calorimetry Experiment Error

A student performs a calorimetry experiment to determine the specific heat capacity of a metal sampl

Statistical Interpretation of Gas Behavior

The kinetic theory of gases connects microscopic molecular behavior with macroscopic properties. Two

Transient Heat Conduction in a Rod

A researcher studies transient (time-dependent) heat conduction in a long rod that is initially at a

Understanding Thermal Equilibrium and the Zeroth Law

The Zeroth Law of Thermodynamics states that if object A is in thermal equilibrium with object B, an

Verification of RMS Speed Dependence on Temperature

An experiment measured the RMS speed of gas molecules at different temperatures, with the following

Work Calculation in Sequential Thermodynamic Processes

A gas undergoes a two-step process: an isobaric expansion followed by an isochoric heating. Using th

Work Done in a Non-Constant Pressure Process

An ideal gas is compressed in a cylinder by a piston, and the pressure inside the cylinder varies wi

Analysis of a Parallel-Plate Capacitor

A parallel-plate capacitor has a capacitance of $$10 \; nF$$ and holds a charge of $$50 \; \mu C$$ o

Analyzing Electric Field Variation Above a Charged Plate

An experiment measured the electric potential at various distances from a large, uniformly charged p

Application of Coulomb's Law

Coulomb’s Law states that the magnitude of the electric force between two point charges is given by

Balancing Forces in a Uniform Electric Field

An object of mass $$5.0 \; g$$ (0.005 kg) is placed 2.0 cm above a large, positively charged horizon

Balancing Forces in a Uniform Electric Field

In an experiment to study the balance between gravitational and electric forces, a charged object of

Charge Quantization and Experimental Uncertainty

In a series of experiments, students measured the net charge on several isolated metallic spheres us

Charged Object Equilibrium in a Uniform Electric Field

An experiment is set up to determine the amount of charge required on a small object so that the upw

Comparison of Dipole and Monopole Field Mapping

A simulation experiment compares equipotential maps for a single point charge (monopole) and for a d

Dipole Electric Field Analysis

This question examines the calculation and analysis of the electric field created by an electric dip

Effect of a Dielectric on Capacitor Capacitance

A parallel-plate capacitor with capacitance C₀ is filled with vacuum. (a) If a dielectric material

Effect of Plate Separation on Capacitance in a Parallel-Plate Capacitor

A parallel-plate capacitor is constructed with plates of area A = 0.02 m². The separation between th

Effects of Dielectrics on Capacitor Performance

A capacitor with an initial capacitance $$C_0$$ has a dielectric material with a dielectric constant

Electric Charge Distribution on Conductors: Capacitance Influence Error

In an experiment aimed at studying charge distribution, two metallic spheres of different radii are

Electric Dipole Field Analysis

A dipole is composed of two point charges, $$+Q$$ and $$-Q$$, each of magnitude $$4.0\;nC$$, separat

Electric Field Due to a Uniformly Charged Rod

A thin rod of length 0.5 m carries a uniform linear charge density of $$\lambda = 2.0*10^{-6}$$ C/m.

Electric Field Lines at Media Boundaries

This problem examines how electric field lines behave at the boundary between two different media an

Electric Field Mapping Using Discrete Data Points

A student conducts an experiment to measure the electric field around a set of point charges by firs

Electric Force Sensor Alignment Experiment

A student uses an electric force sensor mounted on a pivot to measure the net force on a test charge

Electric Potential Energy Conversion in a Point Charge Field

A positive charge is released from rest at a distance of 10 cm from a fixed positive charge and is l

Experimental Mapping of Electric Field Lines in a Uniform Field

Design an experiment to map the electric field lines and equipotential regions between two large par

Force Comparison in Hydrogen Atom

A researcher compares the electric and gravitational forces between the proton and electron in a hyd

Force on Test Charge in a Uniform Electric Field

A test charge of $$+3.0*10^{-9}$$ C is placed in a uniform electric field of magnitude 400 N/C that

Investigating Capacitor Energy Storage Versus Separation Distance

Design an experiment to measure how the energy stored in a parallel-plate capacitor changes as the d

Investigating Coulomb's Law in a Controlled Experiment

Design an experiment to measure the electric force between two charged spheres as a function of sepa

Kinetic Energy Gain from Electric Potential Energy Loss

A negative charge of magnitude q = -1×10⁻⁸ C is released from rest at a distance of 10 cm from a fix

Mapping Equipotential Surfaces in a Non-uniform Electric Field

In a region of space, the electric potential has been measured at various distances from a fixed cha

Motion of a Charged Particle in a Uniform Electric Field

A small charged particle with charge q = 2.0×10^-6 C and mass m = 2.0×10^-3 kg is released from rest

Potential Energy Change in a Non-Uniform Field

A test charge moves in the electric field of a fixed point charge. Using the concept of electric pot

RC Circuit Charging

A researcher investigates the charging behavior of a capacitor in an RC circuit. The circuit contain

Superposition of Electric Fields: Square Charge Configuration

Four identical positive point charges are fixed at the vertices of a square with side length 0.20 m.

Superposition of Forces in a Square Configuration

Four equal positive point charges are placed at the vertices of a square. A negative charge is place

Uniform Electric Field Balance Experiment

A large, positively charged horizontal plate produces a uniform electric field of magnitude $$E = 1.

Work Done and Change in Electric Potential Energy

A particle with charge $$q = +3.0 \times 10^{-9} \; C$$ is displaced by $$0.05 \; m$$ in the directi

Work Done in a Non-uniform Electric Field

A charged particle experiences a non-uniform electric field given by $$E(y) = 200 \; y \quad (N/C)$$

Work Required to Assemble a Triangular System of Point Charges

Three point charges are fixed in place forming a triangle. The charges and separations are: Q₁ = +2.

Analysis of Ammeter and Voltmeter Placement

This question addresses the proper usage of ammeters and voltmeters in a circuit for accurate measur

Analyzing the Effect of Wire Geometry on Resistance Measurements

A student investigates how the resistance of a wire depends on its length and cross-sectional area b

Application of Kirchhoff’s Junction and Loop Rules

Consider a circuit where three branches intersect at a junction. Two branches carry currents $$I_1$$

Application of Kirchhoff’s Laws in Complex Circuits

Consider a circuit that has two branches: one branch contains a single resistor and the other branch

Battery and Capacitor in Renewable Energy Applications

In a simplified model of a solar panel energy storage system, a battery with an ideal EMF of 18 V an

Battery Internal Resistance and Terminal Voltage

A study claims that the terminal voltage of a battery decreases noticeably when a load is connected

Battery Performance and Power Output

A 12 V battery is connected to a resistor, and its terminal voltage, current, and power output are r

Capacitance Modification in Connected vs. Disconnected Batteries

A capacitor with capacitance $$C = 20\,\mu F$$ is charged in a circuit. Compare and contrast two sce

Capacitor Charging and Discharging in RC Circuits

An experiment claims that when a charged capacitor discharges through a resistor, the voltage across

Capacitor Charging Experiment in an RC Circuit

A student assembles an RC circuit that includes a 12 V battery, a 3 Ω resistor, and an initially unc

Capacitor Combinations and Equivalent Capacitance

A circuit contains three capacitors with the following capacitances: 4 μF, 6 μF, and 12 μF. In the c

Circuit Design and Optimization: An Integrated Approach

Design a circuit that delivers a steady current of $$2~A$$ to a load while minimizing power loss and

Deriving Equivalent Resistance for a Mixed Circuit

Consider a circuit comprised of four resistors arranged as follows: Resistors R₁ = 100 Ω and R₂ = 15

Design and Analysis of a Flash Circuit for a Camera

A camera flash circuit uses a capacitor with capacitance $$C = 100\,\mu F$$, charged by a 300 V batt

Design of an Experiment: Measuring Capacitance

Design an experiment to accurately measure the capacitance of a parallel-plate capacitor. Your desig

Designing a Resistor Network for Specific Equivalent Resistance

You are provided with resistors of values $$5 \Omega$$, $$10 \Omega$$, and $$15 \Omega$$. Design a r

Determination of Material Resistivity

A student is conducting an experiment to determine the resistivity of wires made from different mate

Discharging of a Capacitor in an RC Circuit

A capacitor initially charged to $$12 \text{ V}$$ is discharged through a resistor of $$4 \Omega$$.

Evaluating Conductance and its Relationship to Resistance

Electrical conductance, the reciprocal of resistance, is an important parameter in circuit analysis.

Evaluating Power Dissipation in a Resistor Circuit

A student constructs a simple circuit using a 9 V battery and a 10 Ω resistor to compute power dissi

Evaluation of Circuit Performance with a Faulty Capacitor (Capacitor Failure Analysis)

A capacitor in an RC circuit, which is expected to be 47 μF, is suspected of being faulty due to lea

Evaluation of Energy Storage in a Capacitor

A capacitor with a capacitance of 10 μF is charged to a potential difference of 12 V.

Graph Analysis: Charging Behavior in an RC Circuit

A graph is provided showing the voltage across a capacitor as a function of time while it charges in

Impact of Temperature on Battery Performance

Temperature can impact battery performance by altering its internal resistance.

Impact of Temperature on Resistor Performance

A researcher investigates how the resistance of a metallic resistor changes as the temperature is in

Investigating Non-Ohmic Behavior in an AC Circuit

A student conducts an experiment on an incandescent light bulb powered by a 120 V AC source and atte

Investigating the Impact of Wire Geometry on Electrical Resistance

A claim is made that the resistance of a wire depends on its length and cross-sectional area as desc

Kirchhoff's Laws in Multi-Loop Circuits

In a multi-loop circuit, measurements of current at various junctions are taken. Use Kirchhoff’s law

Oscilloscope Analysis of Voltage Drops in a Circuit

An oscilloscope is used to measure the voltage drops across various components in a circuit consisti

RC Circuit Analysis with Switch Operations

In an RC circuit with a switch, experimental measurements indicate that immediately after closing th

RC Circuit: Charging and Discharging of a Capacitor

A timing circuit consists of a resistor and a capacitor connected in series with a 12 V battery via

Resistivity and Material Properties

In a study of different conductive materials, wires of identical dimensions (length = 2 m, cross-sec

Resistor Networks and Equivalent Resistance

A circuit contains three resistors arranged in a mixed series-parallel configuration. Resistors R1 =

Series and Parallel Circuit Analysis

In this problem, you will analyze a circuit that comprises a combination of resistors in both series

Series Circuit Analysis and Ohm's Law Application

A battery of 9 V is connected in series with two resistors: one having a resistance of 100 Ω and the

Transient Behavior in RC Circuit: Initial vs Steady-State

An RC circuit is constructed with a $$12~V$$ battery, and two branches: one branch contains a $$6~\O

AC Generator Induced EMF Analysis

Consider an alternating current generator where a coil of $$N$$ turns and area $$A$$ rotates in a un

AC Generator: Maximum Induced EMF Calculation

In a simple AC generator, a coil with 50 turns and an area of 0.2 m² rotates in a uniform magnetic f

Analyzing Magnetic Field Lines with Iron Filings

This FRQ requires analyzing the patterns formed by iron filings around a bar magnet, emphasizing the

Angular Dependence of Magnetic Force

A series of experiments measures the magnetic force on a charged particle moving in a constant magne

Assessing Iron Dust Experiments for Bar Magnets

A study uses iron dust to demonstrate that the magnetic field inside a bar magnet is continuous and

Calculating Magnetic Flux in a Non-Uniform Magnetic Field

A rectangular loop with width $$w = 0.2$$ m and height $$h = 0.3$$ m is placed in a magnetic field t

Circular Motion of a Charged Particle in a Magnetic Field

A charged particle enters a uniform magnetic field perpendicular to its velocity and undergoes unifo

Current-Carrying Wire Force Experiment

A group of students conducts an experiment to measure the force on a U-shaped current-carrying wire

Deflection of Charged Particles in Crossed Fields

In an experiment, charged particles are passed through a region where perpendicular electric and mag

Dependence of Induced EMF on Rotation Rate

A circular loop rotates continuously in a uniform magnetic field, thereby inducing an emf that varie

Effect of Changing Magnetic Field Strength on Induced Current

A coil is subjected to a magnetic field that decreases linearly from $$B_0$$ to $$B_1$$ over a time

Electromagnetic Induction in a Rotating Loop

A single-turn wire loop with an area of $$A = 0.05 m^2$$ is placed in a uniform magnetic field of ma

Energy Transformation in a Moving Conductor Experiment

In an experiment, a conducting bar is made to slide through a uniform magnetic field, generating an

Evaluating Solenoid Field Uniformity

In an experiment, the magnetic field inside a solenoid is measured at different positions along its

Experimental Verification of Lenz's Law

Design an experiment to verify Lenz's Law by demonstrating that the direction of the induced current

Experimental Verification of the Right-Hand Rule

Design an experiment to verify the right-hand rule by measuring the direction of the magnetic force

Impact of Magnetic Field Reversal on Induced EMF

Consider a single-turn loop in which the magnetic flux initially is $$\Phi_i = B*A$$. If the externa

Induced EMF in a Rectangular Loop Under Rotation

A rectangular loop of wire measuring 0.1 m by 0.2 m is placed in a uniform magnetic field of 0.5 T.

Induced EMF in a Sliding Rod Circuit

Consider a circuit formed by a sliding rod of length $$\ell$$ that moves on conducting rails, comple

Induced EMF in a Time-Varying Solenoid Field

A solenoid with 300 turns and a cross-sectional area of 0.05 m² produces an axial magnetic field tha

Investigating Magnetic Braking in a Rotating Disc

In this experiment, students study magnetic braking by rotating a metallic disc in the vicinity of a

Magnetic Braking in a Rotating Metal Disk

A metal disk is set into rotation and brought near a set of fixed magnets arranged so that eddy curr

Magnetic Field vs. Distance from Wire

A long, straight wire carrying a constant current produces a magnetic field whose strength decreases

Magnetic Flux Change in a Rotating Loop

A circular loop of wire is rotating in a uniform magnetic field, causing a time-dependent change in

Magnetic Force on a Current-Carrying Wire in a U-Shaped Conductor

This FRQ examines the application of the magnetic force formula on current-carrying conductors and e

Magnetic Force on a Moving Charge

A charged particle moves through a uniform magnetic field. Use the relationship that the magnetic fo

Magnetic Force vs. Current in a Wire

An experiment examines the magnetic force acting on a straight current-carrying wire placed in a uni

Magnetic Levitation and Force Equilibrium

Investigate the conditions required for magnetic levitation using magnetic repulsion, and analyze po

Mapping Magnetic Field Lines using Computer Simulation

Students use a computer simulation to model the magnetic field lines around a bar magnet and analyze

Mapping Magnetic Field Using Iron Filings

Students perform an experiment to visualize the magnetic field around a bar magnet by sprinkling iro

Mapping Magnetic Fields around a Bar Magnet

A researcher is studying the magnetic field of a standard bar magnet in a controlled laboratory sett

Measuring Deflections of Compass Needles in a Non-Uniform Magnetic Field

In this experiment, compass needles are placed at various distances from a bar magnet to record the

Measuring Magnetic Permeability Experiment

An experiment is designed to determine the magnetic permeability of a new material. A coil is wound

Motion of a Charge in Perpendicular Electric and Magnetic Fields

A charged particle with charge $$q$$ and mass $$m$$ enters a region where there is a uniform magneti

Motional EMF in a Conducting Rod

A conducting rod of length $$l = 0.2$$ m moves at a constant speed $$v = 3.0$$ m/s through a uniform

Motional EMF in a Sliding Bar Circuit

A U-shaped rail of length 1 m is connected by a sliding conductive bar, forming a rectangular circui

Motional EMF with an Oblique Angle

A conducting rod of length 0.8 m moves with a speed of 4 m/s through a uniform magnetic field of 0.1

Optimizing Solenoid Configuration for Maximum Magnetic Field

An engineer is tasked with designing a solenoid to produce the strongest possible uniform magnetic f

Proton Force Near a Current-Carrying Wire

A proton moves near a long, straight wire carrying a fixed current, and its magnetic force is measur

Testing the Right-Hand Rule for Magnetic Force Directions

An experiment is performed where charged particles are propelled in known directions through a unifo

Advanced Optics: Aberrations and Corrections in Optical Systems

A researcher is analyzing a high-precision imaging system that exhibits spherical aberration due to

Concave Mirror Image Analysis

An object of height $$h_o = 4 \ cm$$ is placed at a distance of $$d_o = 30 \ cm$$ in front of a conc

Concave Mirror Image Characteristics

Concave mirrors can produce images that are real or virtual depending on the object position. Analyz

Converging Lens Experiment: Measuring Focal Length Using Object-Image Distances

Design an experiment to measure the focal length of a converging lens using object and image distanc

Converging Lens Image Formation

A converging lens has a focal length of $$15 \text{ cm}$$, and an object is placed $$25 \text{ cm}$$

Converging Lens Power Measurement: Magnification Error Analysis

A student uses a converging lens to form a real image of an object, records the object and image dis

Determining Lens Power: Experimental Measurement via Object-Image Distance

Design an experiment to determine the power of a converging lens by measuring object and image dista

Diffraction Grating Wavelength Measurement

A student uses a diffraction grating with 5000 lines per centimeter to measure the wavelength of an

Diffraction Gratings Analysis

A diffraction grating with 5000 lines per centimeter is used to analyze sodium light with wavelength

Diverging Lens and Virtual Image Formation

Diverging lenses produce virtual, diminished, and upright images. Analyze the image formation by a d

Electromagnetic Wave Characterization

A researcher studies electromagnetic waves emitted by distant stars, using the fundamental relation

Electromagnetic Wave Oscillation Diagram Analysis

Using the provided diagram showing oscillating electric (E) and magnetic (B) fields of an electromag

Electromagnetic Wave Properties and Polarization

An electromagnetic wave is produced by an oscillating charge in free space. Consider a green light w

Exploring the Relationship Between Frequency and Wavelength

A student conducts an experiment to examine the relationship between frequency and wavelength in dif

Laser Interferometry and Fringe Shift Analysis

A student employs a Michelson interferometer with a coherent laser source (wavelength $$\lambda = 63

Lens Power and Image Size Determination

A converging lens forms a real image that is twice the height of the object when the object is place

Multi-Wavelength Interference Experiment

In an experiment using a diffraction grating, two monochromatic light sources are employed: red ligh

Optical Data Analysis from Spherical Mirror Measurements

An experiment is conducted where an object is placed at various distances from a concave mirror, and

Optical Sensors in Environmental Monitoring

Environmental scientists are developing optical sensors to monitor particulate matter in water. The

Plane Mirror Image Analysis

A researcher investigates image formation by plane mirrors. An object is placed 2.0 m in front of a

Plane Mirror Investigation: Verifying Virtual Image Formation

Design an experiment to investigate how plane mirrors form virtual images. Your design should includ

Polarization and Brewster's Angle

When unpolarized light strikes a glass surface, the reflected light becomes partially polarized. Con

Polarization and Electromagnetic Wave Behavior

In an experiment testing polarization, a polarizer is rotated and the transmitted light intensity is

Properties of Electromagnetic Waves

This question explores the basic properties of electromagnetic waves including their speed, the freq

Radio Waves in Communication

Radio communications often use electromagnetic waves with wavelengths on the order of meters. (a) C

Ray Tracing for Converging Lenses and Mirrors

This question involves constructing ray diagrams for optical instruments. (a) Draw and label a ray

Ray Tracing Verification for Spherical Mirrors

Design an experiment to verify the mirror equation using ray tracing with a concave spherical mirror

Real vs. Virtual Images in Combined Optical Systems

An optical system is constructed by combining a concave mirror with a converging lens. Answer the fo

Reflection and Refraction at an Interface

A beam of light traveling in air (index of refraction $$n_1 = 1.0$$) strikes the surface of a glass

Scattering of Light: Rayleigh Scattering

A graph from an experiment shows how the intensity of scattered light varies with wavelength due to

Single Slit Diffraction Patterns

A monochromatic light of wavelength $$λ = 600*10^{-9} \ m$$ is incident upon a single slit with a wi

Spherical Mirrors and Image Formation

A concave spherical mirror has a radius of curvature of $$20 \text{ cm}$$. An object is placed $$10

Thin Converging Lens Imaging

A bi-convex (converging) lens with a focal length of 10 cm is used to form an image of an object tha

Thin Lenses - Converging Lens Magnification

An object is placed 10 cm in front of a converging lens, resulting in a real image that is twice the

Total Internal Reflection

When light travels from water ($$n = 1.33$$) to air ($$n = 1.0$$), total internal reflection can occ

Total Internal Reflection in Optical Fibers

A set of experiments investigates the conditions under which total internal reflection (TIR) occurs

Young's Double Slit Experiment Analysis

In Young's double slit experiment, coherent light passing through two closely spaced slits produces

Young’s Double Slit Experiment Analysis

A double slit experiment is set up with two narrow slits separated by $$d = 1.5 * 10^{-3}$$ m, a scr

Bohr Model and Atomic Spectra

A researcher is investigating the emission spectrum of a hydrogen-like ion. The energy levels in thi

Calculating Nuclear Binding Energy

A researcher is investigating the stability of nuclei by calculating the nuclear binding energy per

Nuclear Composition and Isotope Identification

A researcher is examining a nuclide represented by $$^{63}_{29}X$$. Using this information, address