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.
Analysis of Electric Field Lines
Examine the following diagram representing electric field lines produced by a positive and a negativ
Analysis of Electric Potential in a Charged Spherical Conductor
In a controlled laboratory setting, students study the electric potential around a charged conductin
Analyzing Transient Response in RLC Circuits Using Calculus-Based Modeling
Design an experiment to study transient oscillations in an RLC circuit. Use calculus to model the di
Applying Gauss' Law for a Spherical Conductor
In a lab experiment, the electric flux through spherical surfaces of various radii is measured aroun
Calculus in Electric Potential Calculation
In a region, the electric field varies along the x-axis as $$E(x) = 500*(1 - 0.5*x) \; N/C$$, where
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 Experiment
A capacitor with capacitance $$C = 10 \; \mu F$$ is charged through a resistor with resistance $$R =
Characterizing Electric Field Strength from a Point Charge
A research lab sets up an experiment where a known point charge is placed at the origin, and a small
Charge Distribution in Insulators and Conductors
Two spheres of radius $$0.10 \; m$$ are considered. One is a non-conducting (insulating) sphere with
Charge Induction on a Conductor
When a positively charged rod is brought near a neutral conductor, charge induction occurs. Analyze
Charging and Discharging of a Capacitor: Calculus Approach
In this question, you will derive and solve the differential equation governing the charging/dischar
Computation of Electric Flux Through a Curved Surface
A curved surface is placed in a uniform electric field. The cumulative electric flux through the sur
Coulomb Interactions in Point Charge Systems
In a vacuum, consider a system of point charges. Use Coulomb's Law to analyze the system.
Coulomb's Law Investigation
In a laboratory experiment, two point charges are placed on an insulating table. One charge has a va
Coulomb's Law Verification Experiment
You are tasked with designing an experiment to verify Coulomb's Law by measuring the force between t
Determining Electric Potential Distribution around a Point Charge
Design an experiment to measure the electric potential at various distances from an isolated point c
Determining Electric Potential from Experimental Measurements
A set-up is used to measure the electric potential at various distances from a point charge. The mea
Dynamics of a Charged Particle in a Non-Uniform Electric Field
A charged particle of mass m and charge q enters a region where the electric field decreases with di
Electric Field Due to a Cylindrical Surface Charge Distribution
Apply Gauss' Law to derive the electric field for a cylindrical charge distribution and then calcula
Electric Field from an Infinite Plane of Charge
A large, flat surface carries a uniform surface charge density of $$\sigma = 3.0*10^{-6} \; C/m^2$$.
Electric Field Gradient and Potential Difference
A group of students measures the spatial distribution of an electric field along a straight line usi
Electric Field in a Non-uniform Charge Distribution on a Plate
An experiment investigates the electric field produced by a non-uniformly charged insulating plate.
Electric Field of a Charged Cylinder
A long cylindrical rod of radius $$R = 0.05 \; m$$ has a uniform volume charge density of $$\rho = 4
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 an Infinite Line Charge
This question guides you through the derivation of the electric field due to an infinite line charge
Electric Flux and Gauss' Law in Different Geometries
Students conduct a computer simulation of electric flux through various closed surfaces, including a
Electric Flux Graph Analysis using Gauss' Law
A laboratory experiment measured the electric flux $$\Phi$$ (in N·m²/C) through closed surfaces for
Electric Flux Through a Composite Surface
Consider a closed surface that is composed of a hemisphere (of radius $$R = 0.20 \; m$$) attached to
Electrostatic Force in an Equilateral Triangle of Charges
This problem examines the net electrostatic force on a charge located at one vertex of an equilatera
Energy Stored in a Parallel Plate Capacitor
A parallel plate capacitor has a plate area A, separation d, and is charged to a potential differenc
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
Exploring Gauss' Law in a Multi-Charged Environment
Students design an experiment in which multiple point charges are arranged inside a closed surface.
Field Inside and Outside a Charged Sphere
A non-conducting sphere of radius $$R = 0.20 \; m$$ carries a uniformly distributed charge of $$Q =
FRQ 1: Evaluation of Coulomb's Law Experiment
A physicist conducted an experiment to measure the electrostatic force between two small charged sph
FRQ 5: Gauss' Law Experiment in a Spherical Cavity
A published study claims that measurements of electric flux within a hollow (but supposedly neutral)
FRQ 7: Experimental Determination of Electric Flux via Gauss' Law
A laboratory report asserts that measurements of electric flux through a cubic surface surrounding a
FRQ 8: Investigating Insulator Polarization Effects
A recent experiment claims that an insulating material exhibits zero internal electric field due to
FRQ 14: Analysis of Electrostatic Force Variation with Distance
A researcher claims that the measured electrostatic force between two point charges precisely follow
Gauss' Law and Cylindrical Charge Distributions
Consider an infinite line of charge with linear charge density $$\lambda$$ and a cylindrical shell w
Gauss' Law for a Non-Uniform Spherical Charge Distribution
Consider a sphere of radius R with a radial dependent charge density given by $$\rho(r) = \rho_0*(r/
Gauss' Law in a Cylindrical Charge Distribution
An infinitely long cylinder of radius R carries a uniform volume charge density ρ. Use Gauss’s law t
Gauss' Law in Practice: Flux Calculation for a Charged Cylinder
Develop an experimental proposal to measure the electric flux through a cylindrical surface surround
Gauss' Law: Spherical Charge Distribution
A point charge is enclosed within a spherical surface. Analyze the electric flux through the sphere
Gauss's Law Applied to an Infinite Sheet
Apply Gauss's law to derive and analyze the electric field of an infinite plane sheet of charge. Res
Gaussian Surface and Electric Flux for a Point Charge
A point charge of $$+2.0*10^{-9} \; C$$ is positioned at the center of a spherical Gaussian surface
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
Investigating Point Charge Interactions Using Coulomb's Law
A researcher is investigating the interactions between two point charges using Coulomb's Law. In her
Multi-Charge Interaction Analysis
Three point charges are located at the vertices of an equilateral triangle with side length $$0.10 \
Net Electric Field from Multiple Point Charges
Three point charges are positioned along the x-axis. The charge and position data is provided in the
Path Integral for Work in a Non-Uniform Electric Field
A charged particle moves in a non-uniform electric field given by $$E(x,y) = (A*x, B*y)$$. The parti
Superposition of Electric Potentials
This problem involves calculating the net electric potential at a point due to two point charges usi
Transient Analysis in an RC Circuit
In an RC circuit, a capacitor of capacitance $$C = 100 \; \mu F$$ is charged through a resistor of r
Uniformly Charged Sphere: Electric Field and Potential
A sphere of radius $$R$$ carries a uniform charge distribution with a total charge $$Q$$. Analyze th
Using Gauss' Law for an Infinite Charged Plane
This question involves applying Gauss' Law to derive and calculate the electric field due to an infi
Work Done by Electric Fields in Moving a Charge
An experiment investigates the work done by a uniform electric field on a test charge as it is moved
Work Done by Electric Fields: Integral Calculation
Electric fields perform work on charges moving through them. Determine the work done in moving a cha
Work Done in a Non-Uniform Electric Field
This question requires you to compute the work done on a charge moving through a spatially varying (
AC Response and Displacement Current in a Capacitor
A capacitor with capacitance $$C$$ is connected to an AC voltage source described by $$V(t) = V_0 \c
AC Response of a Capacitive Circuit with Variable Frequency
A researcher investigates the impedance of a capacitor in an AC circuit across a range of frequencie
Analysis of Capacitors in Series and Parallel
A circuit contains three capacitors arranged such that capacitors $$C_1$$ and $$C_2$$ are connected
Analysis of Faraday Cage Shielding Effectiveness
A Faraday cage is evaluated by measuring the internal voltage while varying the thickness of the con
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 with a Time-Varying Voltage Source
Consider a circuit where a capacitor of capacitance $$C$$ is connected through a resistor $$R$$ to a
Capacitor Discharge Curve and Time Constant Computation
A capacitor in an RC circuit discharges over time, and its voltage follows the equation $$V(t)=V_0 e
Capacitor in a Time-Varying External Electric Field
A parallel plate capacitor is placed in an external time-varying electric field given by $$E_{ext}(t
Charge Distribution on an Irregular Conductor
An irregularly shaped conductor exhibits a non-uniform surface charge density $$\sigma(x,y)$$. It is
Comparative Analysis of Capacitor Types in High-Frequency Applications
Different types of capacitors (ceramic, electrolytic, and film) exhibit varying performance characte
Derivation of Capacitance Change Due to Temperature-Dependent Dielectric
The dielectric constant of a capacitor material is temperature-dependent, given by $$k(T)=k_i+\delta
Design and Analysis of a Capacitor Bank for Energy Storage
For a high-energy application, a capacitor bank must be designed to store 1000 joules of energy at 1
Designing a Faraday Cage for Sensitive Instrumentation
A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo
Designing a Faraday Cage for Sensitive Instruments
A research team is tasked with designing a Faraday cage to protect sensitive electronic equipment fr
Dielectric Effects on Capacitor Performance
A parallel plate capacitor is initially filled with air. A dielectric slab of thickness $$d$$ and di
Dielectric Strength and Material Breakdown Analysis
A capacitor with a dielectric material of thickness \(d\) is subject to an electric field. The diele
Discharge Analysis of a Capacitor
A capacitor of capacitance $$C$$, initially charged to a voltage $$V_0$$, is allowed to discharge th
Dynamic Parallel Plate Capacitor
A parallel plate capacitor is charged to a constant charge $$Q$$ but has a plate separation that inc
Effect of a Dielectric on Breakdown Voltage
A parallel plate capacitor uses air as the dielectric. The dielectric strength of air is approximate
Effect of Dielectrics on Capacitance: A Comparative Study
A researcher investigates the effect of different dielectric materials on the capacitance of a paral
Effects of Surface Roughness on Conductor's Electric Field
A conducting surface exhibits periodic roughness modeled by a sinusoidal function. Analyze how this
Electric Field on the Surface of a Conductor
A researcher is investigating the behavior of electric fields on the surface of a conductor under el
Electric Field Variation Near a Conducting Surface with a Protrusion
A flat conductor possesses a small protrusion, causing a local increase in curvature. Analyze how th
Electric Shielding Effectiveness Experiment
In an experiment designed to evaluate the effectiveness of electric shielding by a Faraday cage, a r
Energy Density Analysis in a Capacitor With a Non-Uniform Electric Field
A capacitor has an electric field that varies with position according to $$E(x) = \frac{V}{d + a \cd
Energy Dissipation in a Discharging Capacitor
A capacitor with initial voltage $$V_0$$ and capacitance $$C$$ discharges through a resistor $$R$$.
FRQ 1: Electric Field Measurement on a Conductive Sphere
An experimental procedure was conducted to measure the electric field on the surface of a conductive
FRQ 1: Electrostatic Equilibrium in Conducting Spheres
In this experiment, a uniformly charged metal sphere is allowed to reach electrostatic equilibrium.
FRQ 2: Faraday Cage Effectiveness Experiment
A Faraday cage experiment was set up by constructing a cage from aluminum foil, intended to shield a
FRQ 5: Faraday Cage Performance Analysis
A Faraday cage is constructed to protect sensitive electronic equipment from electromagnetic pulses
FRQ 9: Dynamic Change in Capacitance with Variable Plate Area Experiment
A researcher conducted an experiment in which the effective area of one plate in a parallel-plate ca
FRQ 10: Charge Distribution on Curved Conductors
An experiment is undertaken to measure the electric field strength at various points on an irregular
FRQ 11: RC Circuit Discharge Dynamics
Students in a laboratory record the voltage across a resistor as a capacitor discharges in an RC cir
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: Mitigating Electromagnetic Interference in Portable Devices
A study is conducted to measure the effectiveness of different smartphone case materials in reducing
FRQ 15: Dielectric Strength Analysis
In a materials laboratory, dielectric breakdown measurements are performed on various insulating mat
FRQ 16: Measurement of Electric Shielding Effectiveness Using a Conductive Film
An experiment was set up to measure the effectiveness of an electric shield composed of a thin condu
FRQ 17: Dynamic Capacitance Variation with Frequency in a Dielectric
In this experiment, a capacitor with an inserted dielectric is connected to an AC voltage source wit
FRQ 19: Modeling Capacitance of a Non-Standard Geometric Capacitor
A researcher built a capacitor with non-parallel, curved plates to investigate how plate curvature a
Gauss's Law and Charge Distribution on a Spherical Conductor
A spherical conductor with a uniform charge distribution is examined by measuring the electric field
Impact of Dielectric Constant on Capacitance
The capacitance of a capacitor is influenced by the dielectric constant of the material between its
Investigating Resistor Heating during Capacitor Discharge
During a capacitor discharge experiment, not only was the voltage across the capacitor measured but
Investigation of Dielectric Breakdown Voltage
A study was conducted to investigate the breakdown voltage of dielectric materials. The breakdown vo
Modelling Electric Fields Around a Spherical Conductor
A spherical conductor carrying a net charge is analyzed to determine the electric field both inside
Partial Dielectric Insertion and Effective Capacitance
Consider a parallel plate capacitor with plate area \(A\) and plate separation \(d\). A dielectric s
RC Circuit Transient Analysis
A capacitor with capacitance $$C$$ is connected in series with a resistor $$R$$ and a constant volta
Surface Charge Density Determination from Measured Electric Fields
Measurements taken along the surface of a conductor indicate that the electric field varies with pos
Time-Dependent Dielectric Breakdown Analysis
A dielectric material of thickness $$d$$ has a breakdown electric field strength $$E_{break}$$. In r
Transient Analysis of Capacitor Charging in RC Circuits
Transient analysis of capacitor charging provides insight into the dynamic behavior of RC circuits.
Transient Response of Electric Field in Shielded Conductors Under Pulsed Voltage
A pulsed voltage is applied to a shielded conductor. The transient response of the internal electric
Variable Dielectric in a Capacitor
A capacitor is made with a dielectric whose property varies along the separation between the plates.
AC Analysis of a Series RLC Circuit
An RLC series circuit operates with an alternating current signal. Analyze its impedance and phase c
Analysis of Time-Varying Inductance in a Circuit
In a circuit, the inductance varies with time as $$L(t)=L_0*(1+0.1*t)$$, where $$L_0=0.5\;H$$. A con
Analyzing Conduction in AC vs DC Circuits
Data was collected from both AC and DC circuits measuring voltage and current across a resistor unde
Battery EMF and Terminal Voltage Analysis
A non-ideal battery has an electromotive force (EMF) of 9 V and an internal resistance of 1 Ω. It is
Capacitor Charging Diagram Analysis
A graph is provided that represents the capacitor charging process in an RC circuit. Analyze the dia
Characterizing a Non-Ideal Battery from Experimental Data
A researcher collects data on a battery’s performance by measuring its terminal voltage under variou
Comparison of Series and Parallel Resistances
A circuit is configured in two ways: In Configuration A, two resistors, R1 = 5 Ω and R2 = 15 Ω, are
Current Divider Analysis in a Parallel Circuit
A current divider in a parallel circuit consists of two resistors, $$R_{1}=10\,\Omega$$ and $$R_{2}=
Current Division in a Parallel Circuit
In a parallel circuit with two resistors, analyze the distribution of current and its sensitivity to
Current Measurement in Series Circuit Experiment
In this experiment, a student investigates the relationship between applied voltage and current thro
Designing a Circuit for Constant Power Output
A circuit designer aims to maintain a constant power output across a variable load resistor. Analyze
Determining Parameters of a Simple Light Circuit
A 60 W incandescent light bulb is rated for 120 V. It can be modeled as a resistor. Answer the follo
Determining the EMF and Internal Resistance of a Battery
This question explores the relationship between a battery's EMF, its terminal voltage under load, an
Discharging Capacitor Experiment with Ignored Resistance Variation
A researcher investigates the discharging behavior of a capacitor in an RC circuit by disconnecting
Effect of Temperature on Resistor Resistance
A resistor's resistance varies with temperature as $$R(T)=R_0*(1+\alpha*(T-T_0))$$, where $$R_0=50\;
Efficiency Analysis in a Renewable Energy Circuit
A renewable energy system incorporates a battery of 50 V connected in series with a load resistor of
Frequency Response in an RLC Circuit
Consider a series RLC circuit with $$R = 10\,\Omega$$, $$L = 0.1\,H$$, and $$C = 100\,\mu F$$ driven
FRQ 3: Parallel Circuit Analysis
A circuit has three resistors connected in parallel to a $$12\,V$$ battery. The resistors have value
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 11: AC Frequency Analysis in an RLC Circuit
A series RLC circuit has a resistor of $$10\,\Omega$$, an inductor of $$0.5\,H$$, and a capacitor of
FRQ 16: Circuit Measurement Techniques
In a laboratory setting, students are asked to measure voltage, current, and resistance in a circuit
Impact of Capacitance on RC Circuit Time Constant
This question focuses on the effect of capacitance on the RC time constant, integrating both theoret
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
Investigating the Effect of Variable Resistance on Circuit Current
A variable resistor (potentiometer) is used in a DC circuit powered by a 12 V battery. Experimental
Kirchhoff's Loop Analysis
Analyze a circuit consisting of two loops sharing a common resistor. The circuit has two voltage sou
KVL and Energy Conservation in a Closed Loop
A student asserts that, in any closed circuit loop, the algebraic sum of the voltage drops is exactl
Measuring Circuit Parameters with Multimeter and Oscilloscope
A technician uses a multimeter and an oscilloscope to determine various circuit parameters. Analyze
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
Oscilloscope Analysis of an AC Signal
An oscilloscope displays the waveform of an AC signal. Use the provided trace to analyze its charact
Oscilloscope Data Analysis in Circuit Diagnostics
In an electronics lab, an oscilloscope is used to record the voltage waveform across a resistor. The
Parallel Circuit Analysis with Exponential Resistance Change
A researcher investigates a parallel circuit where three branches contain resistors whose resistance
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 Non-Ideal Battery Analysis
Examine a circuit where a non-ideal battery with an electromotive force (EMF) of $$\mathcal{E} = 12\
RC Circuit Charging and Discharging Analysis
An RC circuit consists of a resistor $$R$$ and a capacitor $$C$$ connected in series with a battery
RC Low-Pass Filter Frequency Response Analysis
A research group hypothesizes that an RC low-pass filter attenuates high-frequency signals such that
RC Oscillator Analysis
An RC oscillator circuit is designed to produce a periodic square wave. The oscillation period \(T\)
RC Oscillator Design
An RC oscillator utilizes an RC network to generate periodic signals. The frequency of oscillation i
Resistance Measurements and Conductor Geometry
A uniform wire with a length L = 2 m and cross-sectional area A = 1 mm² (1×10⁻⁶ m²) is made of a mat
Resonance and Quality Factor in an LCR Circuit
A researcher examines an LCR series circuit comprising an inductor $$L=0.1\,H$$, a capacitor $$C=100
RLC Circuit Resonance
An RLC series circuit exhibits resonance at a specific frequency. Analyze the resonance behavior in
Series and Parallel Circuits Analysis
Consider a circuit that consists of a voltage source $$V_0 = 12\,V$$ connected to a network containi
Series Circuit with Non-Ideal Battery Analysis
Consider a circuit consisting of a non-ideal battery with electromotive force $$\mathcal{E}$$ and in
Temperature Effects on Resistance
A researcher investigates how temperature affects the resistance of a thermistor. The experiment mea
Testing the Superposition Principle in Linear Circuits
This question examines the application of the superposition principle in circuits with multiple inde
Transient Behavior in a Combined RC and RL Circuit
A researcher studies a circuit that combines elements of both RC and RL circuits. In this circuit, t
Transient Response in RC Charging Circuit
In an RC circuit with resistor R = 10 Ω and capacitor C = 100 μF, the capacitor is initially uncharg
Variable Resistor and Thermistor Behavior Analysis
A variable resistor in a circuit is adjusted to change its voltage drop linearly with rotation. Addi
Voltage Divider Circuit Analysis
A voltage divider is constructed using two resistors, \(R_1\) and \(R_2\), connected in series acros
Voltage Division in Series Circuits
This question examines your understanding of voltage division in series circuits and your ability to
Ampère’s Law in a Toroid
A researcher designs a toroid and wishes to determine the magnetic field inside its core. Given the
Ampère’s Law with Non-Circular Symmetry
A rectangular loop is placed in a magnetic field that has a linear gradient. A researcher aims to de
Analysis of Torque on a Wire in a Magnetic Field
A wire carrying current is placed in a magnetic field and experiences a torque. A graph of applied t
Application of Ampère’s Law in Complex Loops
Consider a closed loop formed by a current-carrying wire that is not circular. Parts of the loop exp
Application of the Right-Hand Rule
A straight, horizontal wire carries a current of $$5 * A$$ from left to right. Using the right-hand
Bar Magnet Field Distribution Analysis
Design an experiment to map the spatial distribution of the magnetic field around a bar magnet. Incl
Calculus of Magnetic Field Lines
A researcher wishes to derive a differential equation that describes the magnetic field lines around
Combined Effect of Electric and Magnetic Fields on a Charged Particle
An experiment claims that when a charged particle moves in a region containing both electric and mag
Combined Electric and Magnetic Field Effects on a Charged Particle (Velocity Selector)
A charged particle is introduced into a region where it experiences both perpendicular electric and
Critical Evaluation of Magnetic Field Uniformity in Solenoid Experiments
A recent experimental study claims that the magnetic field inside a solenoid is perfectly uniform, a
Design Considerations for an Electric Motor Component
Electric motors use current-carrying loops in magnetic fields to generate torque. Consider the desig
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
Determining Torsional Stiffness from Experimental Data
A wire is subjected to various applied torques causing it to twist by different angles θ. The torsio
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 Geometry on Magnetic Field Distribution
Consider two wires carrying the same current I: one is a straight wire and the other is bent into a
Effect of Wire Orientation on Lorentz Force
An experiment investigates how the orientation of a current-carrying wire in a magnetic field affect
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 Investigation of Force Between Parallel Current-Carrying Wires
An experiment is conducted to verify the force between two parallel current-carrying wires. The wire
Force Between Parallel Current-Carrying Wires
Two long, parallel wires separated by a distance \(d\) carry currents \(I_1\) and \(I_2\). They exer
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 on a Current-Carrying Wire
Investigate the force experienced by a current-carrying wire in a uniform magnetic field and analyze
Force on a Current-Carrying Wire in a Magnetic Field
A wire of length L = 0.5 m carrying a current of I = 6 A is placed in a uniform magnetic field of B
Force on a Current-Carrying Wire in a Magnetic Field
A wire of length $$L$$ carrying a current $$I$$ is placed in a uniform magnetic field $$B$$ making a
Force on a Current-Carrying Wire in a Non-Uniform Magnetic Field
Consider a straight wire of length $$L$$ carrying a constant current $$I$$ along the x-axis. The wir
Force on a Current-Carrying Wire in an External Magnetic Field
An experiment measured the force on a current-carrying wire placed in an external magnetic field at
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 Torsional Stiffness Using a Twisted Wire
A wire is subjected to a torsional force generated by magnetic interactions, and its torsional stiff
Magnetic Dipole-Dipole Interaction Energy
Consider two magnetic dipoles, each with magnetic moment $$m$$, separated by a distance $$d$$. Using
Magnetic Field Distribution around a Bar Magnet
A bar magnet produces a magnetic field that is strongest near its poles. Explore the variation in fi
Magnetic Field in a Circular Loop - Claim Evaluation
A recent research paper claims that the magnetic field produced inside a circular current-carrying l
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 in a Toroid
A toroid with N turns is used to study the magnetic field inside it. The field is theoretically give
Magnetic Field Inside a Toroid
A toroid with N turns carrying a current I has a mean radius R. (a) Derive the expression for the
Magnetic Field Mapping in a Non-Uniform Field
An experiment measures the magnetic field at various distances from a single current-carrying wire.
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
Magnetic Field of a Straight Conductor - Claim Evaluation
A recent popular science article claims that the magnetic field \(B\) around a long, straight curren
Magnetic Field of a Straight Conductor: Right-Hand Rule and Calculation
A long, straight wire carries a current of 3 A in the positive x-direction. (a) Use the right-hand r
Magnetic Field on the Axis of a Circular Current Loop
Using the Biot-Savart Law, derive and analyze the expression for the magnetic field at points along
Magnetic Field Shielding using Superconductors
A superconducting ring of radius 0.1 m is used to shield a region from an applied external magnetic
Measurement of Torsional Stiffness in a Twisted Wire
Design an experiment that uses a twisted wire in a magnetic field to measure its torsional stiffness
Measuring the Lorentz Force on a Moving Charged Particle
A charged particle with charge $$q = 1.6 \times 10^{-19}\,C$$ is accelerated to a velocity of $$2 \t
Net Magnetic Field in a Helmholtz Coil Setup
A Helmholtz coil consists of two identical circular coils of radius 0.12 m, separated by 0.12 m alon
Oscillatory Motion of a Current Loop in a Magnetic Field
A rectangular current loop suspended in a uniform magnetic field experiences a torque which causes i
Torque on a Current Loop
A rectangular loop carrying a current is placed in a uniform magnetic field. (a) Derive an express
Uniform Magnetic Field in a Solenoid
A research team is designing a solenoid for an experiment that requires a uniform magnetic field. Th
Analyzing Displacement Current in a Charging Capacitor
In a parallel-plate capacitor being charged by a current $$I$$, the electric field between the plate
Back EMF Analysis in an LR Circuit
A circuit consists of an inductor (L = 0.05 H) and a resistor (R = 2 Ω) in series. Initially, the ci
Coupled Inductors and Mutual Inductance in Transformers
A researcher examines a transformer system with two coupled inductors to study mutual inductance and
Critical Review of Transformer Data
An experiment on transformers claims high efficiency in flux transfer between the primary and second
Derivation of the Electromagnetic Wave Equation
Starting from Maxwell's equations in free space, derive the wave equations for both the electric fie
Designing an Electromagnetic Braking System
Electromagnetic braking systems use induced currents to generate a retarding force in moving vehicle
Effects of Coil Turns on Inductance
An experiment is conducted wherein the number of turns $$N$$ of a solenoid is varied while its induc
Electromagnetic Generator Analysis
A simple AC generator consists of a rectangular loop with area $$A=0.10\;m^2$$ rotating in a uniform
Energy Storage in an Inductor
An inductor with inductance $$L=0.50\;H$$ carries a time-dependent current given by $$I(t)=5t\;(A)$$
Energy Stored in an Inductor
An inductor of inductance $$L$$ carries a current $$I$$. The energy stored, $$W$$, is obtained by in
Impact of Core Material on Transformer Performance
This problem focuses on how the choice of core material affects transformer performance through its
Induced EMF from Changing Magnetic Flux
A loop experiences a time-dependent magnetic flux given by $$\Phi(t) = \Phi_0 e^{-k*t}$$. Solve the
Induced EMF in a Rotating Loop
A rectangular loop of area $$A$$ rotates with constant angular velocity $$\omega$$ in a uniform magn
Inductance Calculation via Flux Integration
An experiment is conducted where a magnet approaches a coil and induces an EMF that is recorded as a
Inductance in an LR Circuit
An LR circuit is constructed with an inductor of unknown inductance $$L$$ and a resistor of resistan
Induction Heating and Eddy Current Analysis
An induction heater uses electromagnetic induction to heat a metal object. The magnetic flux through
Induction Heating and Eddy Currents
In an induction heating device, a time-varying magnetic field is produced by an alternating current
Induction Heating Performance Test
In an induction heating experiment, a metal sample is placed inside an oscillating magnetic field ge
Investigation of Magnetic Flux Variation with Coil Orientation
An experiment is set up where a coil rotates at constant angular speed in a uniform magnetic field.
LC Circuit Resonance and Energy Oscillations
A student constructs an LC circuit where an inductor and a capacitor exchange energy, resulting in o
Magnetic Field in a Toroid via Ampere's Law
Consider a toroid with $$N$$ turns and a mean radius $$r$$. Use Ampere's law to determine the magnet
Magnetic Field Measurement in a Solenoid
An experiment is carried out to map the magnetic field inside a long solenoid using a Hall probe. Th
Magnetic Flux in a Tilted Coil
A coil is placed in a uniform magnetic field B and its magnetic flux is given by Φ = B * A * cos(θ),
Magnetic Flux Measurement in a Coil
An experiment is designed to measure the magnetic flux through a coil as a magnet is moved toward it
Magnetic Flux Measurement Using a Hall Sensor
A Hall sensor is used to measure the magnetic flux through a loop as it rotates in a uniform magneti
Magnetic Flux Variation Under Sinusoidal Field
A coil is exposed to a time‐varying magnetic field such that its magnetic flux is given by $$\Phi(t)
Magnetic Levitation Analysis
Evaluate a magnetic levitation system where an object of mass $$m$$ is levitated by electromagnetic
Magnetic Levitation Using Electromagnetic Induction
A magnetic levitation (maglev) system uses electromagnets to levitate a train. As the train moves, a
Magnetic Levitation via Electromagnetic Induction
In a magnetic levitation system, coils are used to create dynamically varying magnetic fields that i
Measurement of Magnetic Field Using a Hall Sensor
Design an experiment to measure the magnetic field around a current-carrying wire using a Hall senso
Resonant Frequency in LC Circuits
This problem involves the analysis of an LC circuit and the determination of its resonant frequency.
Rotating Coil Generator Experiment
A graduate student designs an experiment using a rotating rectangular coil placed in a uniform magne
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
Time-Dependent Analysis of LR Circuit with Back EMF
This problem addresses the transient response in an LR circuit with emphasis on back EMF generated b
Time-Dependent Magnetic Field and Flux Calculation
A square loop of side length $$L$$ is placed in a region where the magnetic field is changing with t
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
Transformer Design and Analysis
A transformer is designed to step down an input voltage $$V_{p}$$ to an output voltage $$V_{s}$$. Th
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 N₁ = 1000 turns and a secondary coil of N₂ =
Transformer Efficiency Experiment
A researcher investigates a transformer by varying the number of turns in the secondary coil while k
Transformer Efficiency Investigation
This problem examines the relationships in an ideal transformer and explores how various factors aff
Transformer Voltage Analysis
A transformer consists of two windings: a primary coil with $$N_1$$ turns and a secondary coil with
Transient Response of an LR Circuit
A researcher studies an LR circuit comprised of a resistor (R) and an inductor (L) in series with a
Verification of Faraday's Law in a Coil
In an experiment to verify Faraday’s Law, a coil is placed in the proximity of an electromagnet whos
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Note Tips from Former AP Students
- 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.