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 Linear Charge Distribution in a Rod
A uniformly charged rod is oriented horizontally. The electric field is measured along the perpendic
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
Calibrating an Electroscope: Charging and Discharging Phenomena
Design an experiment to calibrate an electroscope by studying its charging and discharging behavior.
Capacitor Charging Experiment
A capacitor with capacitance $$C = 10 \; \mu F$$ is charged through a resistor with resistance $$R =
Charge Distribution and Conservation Principles
A neutral metallic sphere is charged by transferring electrons from a negatively charged rod. After
Charge Interaction in Mixed Media
A computer simulation investigates how two point charges interact when placed in media with differen
Deriving the Electric Field from a 2D Potential Function
Given a two-dimensional electric potential function, derive the corresponding electric field vector
Deriving the Potential Difference across a Parallel Plate Capacitor
This problem involves using the definition of electric potential to derive the potential difference
Determining Electric Potential from Experimental Measurements
A set-up is used to measure the electric potential at various distances from a point charge. The mea
Determining Surface Charge Density on a Conductor
An experiment is conducted to determine the surface charge density on a conductor by measuring the e
Dynamic Analysis of Discharging Capacitor with Electric Field Measurements
In a classroom experiment, students analyze the discharging process of a capacitor by measuring the
Electric Dipole in a Uniform Electric Field
An electric dipole with dipole moment $$p$$ is placed in a uniform electric field $$E$$ such that th
Electric Field Along the Axis of a Charged Ring
A thin ring of radius $$R$$ carries a uniform charge Q distributed evenly along its circumference. D
Electric Field Behavior in a Uniformly Charged Sphere
A uniformly charged sphere with radius 0.25 m is examined. The electric field strength is measured a
Electric Field in a Cylindrical Charge Distribution
This problem involves using Gauss's law to analyze a cylindrical charge distribution. Provide detail
Electric Field Mapping with a Charged Sphere
An experimenter seeks to measure the electric field produced by a uniformly charged metallic sphere.
Electric Field of a Charged Ring: A Calculus Approach
A ring of radius $$R$$ carries a uniform charge distribution with total charge $$Q$$. Determine the
Electric Field of a Conducting Sphere
A conducting sphere of radius R is uniformly charged with total charge Q. Answer the following quest
Electric Field Variation Graph Analysis
A graph is provided that shows how the electric field strength $$E$$ (in N/C) varies with the distan
Electric Flux and Gauss' Law in Different Geometries
Students conduct a computer simulation of electric flux through various closed surfaces, including a
Electric Flux Through a Composite Surface
Consider a closed surface that is composed of a hemisphere (of radius $$R = 0.20 \; m$$) attached to
Electric Potential from a Point Charge
A point charge $$Q = +3.0*10^{-9} \; C$$ is located at the origin. Answer the following:
Electrostatic Equilibrium in Conductors
A researcher investigates the behavior of electric charges in a conductor connected to a voltage sou
Energy Considerations in Bringing Charges from Infinity
Analyze the work done by an external agent in assembling a two-charge system from infinity to a fini
Energy Stored in a Parallel Plate Capacitor
A parallel plate capacitor has a plate area A, separation d, and is charged to a potential differenc
Error Analysis in Coulomb’s Constant Measurement Experiment
Design an experiment to measure Coulomb’s constant (k) by analyzing the force between charged object
Evaluating the Effects of Dielectric Materials on a Capacitor
In this problem, you will derive the capacitance of a parallel plate capacitor both in vacuum and wh
Experimental Verification of Charge Conservation in Circuit Dynamics
Design an experiment to verify the conservation of electric charge in a closed circuit containing a
Exploring Gauss' Law in a Multi-Charged Environment
Students design an experiment in which multiple point charges are arranged inside a closed surface.
Field and Potential from an Infinite Sheet of Charge
An infinite sheet has a uniform surface charge density of $$\sigma = 4.0 \times 10^{-6} \; C/m^2$$.
FRQ 1: Evaluation of Coulomb's Law Experiment
A physicist conducted an experiment to measure the electrostatic force between two small charged sph
FRQ 7: Experimental Determination of Electric Flux via Gauss' Law
A laboratory report asserts that measurements of electric flux through a cubic surface surrounding a
FRQ 8: Investigating Insulator Polarization Effects
A recent experiment claims that an insulating material exhibits zero internal electric field due to
FRQ 14: Analysis of Electrostatic Force Variation with Distance
A researcher claims that the measured electrostatic force between two point charges precisely follow
FRQ 20: Analysis of Measurement Errors in Field Strength from Extended Charge Distribution
A research team reports that the calculated electric field from an extended planar charge distributi
Gauss' Law and Cylindrical Charge Distributions
Consider an infinite line of charge with linear charge density $$\lambda$$ and a cylindrical shell w
Gauss' Law with a Cylindrical Charge Distribution
A researcher is examining the electric field produced by a long, uniformly charged cylinder with rad
Insulator Polarization Experiment
An experiment is designed to study the polarization effects in an insulating material subjected to a
Integration to Determine Electric Potential along a Line
A uniformly charged rod creates an electric potential along its axis. Determine this potential using
Mapping Electric Field in a Complex Geometry via Monte Carlo Integration
An experiment is performed to map the electric field in a region with a complex charge distribution
Mapping Equipotential Lines and Electric Fields Around Complex Charge Distributions
Design an experiment to map equipotential lines around a complex electrode configuration. Use your e
Net Electric Field from Multiple Point Charges
Three point charges are positioned along the x-axis. The charge and position data is provided in the
Non-uniform Charge Density in a Sphere
A sphere of radius $$R = 0.30 \; m$$ carries a non-uniform volume charge density given by $$\rho(r)
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
Potential from a Line of Charge with Variable Density
A rod extends along the x-axis from $$x = 0$$ to $$x = 0.8 \; m$$. Its linear charge density is give
Superposition Principle in Electric Fields
Two point charges are fixed in space: $$q_1 = +2.5*10^{-9} \; C$$ is at (-0.1 m, 0) and $$q_2 = +1.5
Transient Analysis in an RC Circuit
In an RC circuit, a capacitor of capacitance $$C = 100 \; \mu F$$ is charged through a resistor of r
Work Done by a Uniform Electric Field
A particle with charge $$q = +1.602*10^{-19} \; C$$ is moved over a distance of $$d = 0.10 \; m$$ in
Work Done by a Variable Electric Field
A test charge $$q$$ is moved along the x-axis through a region where the electric field varies with
Work Done Moving a Charge in a Point Charge Field
A charge q is moved in the electric field of a point charge Q from a distance r₁ to r₂. Using calcul
Work from Electric Potential Difference and Variable Charge
Examine the relationship between work and electric potential energy for a charge moving between two
Analysis of Faraday Cage Shielding Effectiveness
A Faraday cage is evaluated by measuring the internal voltage while varying the thickness of the con
Analyzing Charge Distribution on a Composite Conductor
A researcher explores a composite conductor comprising regions with different curvatures and materia
Capacitor Charging with a Time-Varying Voltage Source
Consider a circuit where a capacitor of capacitance $$C$$ is connected through a resistor $$R$$ to a
Capacitors in AC Circuits with Dielectrics
A researcher analyzes a capacitive circuit with a ceramic capacitor in an AC circuit powered by a si
Charge Distribution on an Irregular Conductor
The distribution of charge on an irregularly shaped conductor is non-uniform. Design an experiment t
Charge Distribution on an Irregular Conductor
An irregularly shaped conductor exhibits a non-uniform surface charge density $$\sigma(x,y)$$. It is
Comparative Analysis of Capacitor Types in High Frequency Circuits
A study was performed to compare different types of capacitors—ceramic, electrolytic, film, and tant
Comparison of Ceramic and Film Capacitors in High-Frequency Applications
Ceramic and film capacitors are commonly used in high-frequency circuits. Their performance can diff
Curvature Effects on Conductor Electric Field Distribution
The electric field on the surface of a conductor is influenced by its local curvature. In a simplifi
Deriving the Zero Electric Field Inside a Conductor
Use Gauss’ law and the boundary conditions at the surface of a conductor to prove that the electric
Design Optimization of a High-Energy Capacitor
Designers want to maximize the energy storage in a capacitor. The energy density is given by $$u = \
Designing a Faraday Cage for Sensitive Instrumentation
A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo
Designing an AC Circuit with a Capacitor and Calculus Analysis
In an AC circuit, the voltage across a capacitor is given by \(V(t) = V_0 * \sin(2 * \pi * f * t)\),
Determining Permittivity from Parallel Plate Capacitor Data
An experiment involving a parallel plate capacitor was conducted to determine the permittivity of th
Discharge Analysis of a Capacitor
A capacitor of capacitance $$C$$, initially charged to a voltage $$V_0$$, is allowed to discharge th
Effect of Dielectrics on Capacitance
A capacitor initially in vacuum with capacitance $$C_0$$ has a dielectric material with dielectric c
Effective Electric Field in a Composite Conductor
An experiment was designed to measure the effective electric field on various regions of a composite
Electric Field Distribution on a Metal Sphere
A metal sphere of radius $$R$$ is uniformly charged with total charge $$Q$$. Answer the following qu
Electric Field in a Multi-Layer Dielectric Capacitor
Consider a capacitor consisting of two dielectric layers in series with thicknesses $$d_1$$ and $$d_
Electric Field on the Surface of a Conductor Investigation
A researcher measures the electric field on the surface of an irregularly shaped conductor. The expe
Electric Shielding Efficiency in a Laboratory Setting
A researcher tests the effectiveness of different conductive materials as electric shields. The shie
Electrostatic Induction on a Spherical Conductor
A spherical conductor of radius \(R\) is placed in the vicinity of an external point charge \(Q\) lo
Energy Density Analysis in a Capacitor With a Non-Uniform Electric Field
A capacitor has an electric field that varies with position according to $$E(x) = \frac{V}{d + a \cd
Energy Storage in a Parallel Plate Capacitor
A parallel plate capacitor is constructed with plates of area $$A$$ separated by a distance $$d$$ an
FRQ 1: Electrostatic Equilibrium in Conducting Spheres
In this experiment, a uniformly charged metal sphere is allowed to reach electrostatic equilibrium.
FRQ 5: Capacitor Energy Storage Measurement with Voltage Ramp Experiment
A student charged a capacitor using a voltage source that increased linearly with time, intending to
FRQ 8: High-Frequency Response of Capacitors
In this experiment, a researcher investigates the performance of ceramic and electrolytic capacitors
FRQ 9: Comparative Analysis of Capacitive Energy Storage
Two identical capacitors are connected in two different configurations: one in series and the other
FRQ 9: Lightning Protection and Faraday Cage Efficacy in Simulated Environments
A controlled laboratory setup is designed to simulate lightning strikes by applying high voltage spi
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 11: RC Circuit Discharge Dynamics
Students in a laboratory record the voltage across a resistor as a capacitor discharges in an RC cir
FRQ 14: Energy Dissipation in a Capacitor Discharge with Temperature-Dependent Resistance
A student conducted an experiment to measure the energy dissipated during the discharge of a capacit
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 17: Influence of Resistance on Capacitor Discharge Rate
In a laboratory, several RC circuits are constructed with a constant capacitance but varying resisto
FRQ 18: Apparent Charge Redistribution in a Connected Conductor System
A researcher investigated charge redistribution between two conductors of different geometries that
FRQ 19: Non-Uniform Electric Fields in a Gradient Dielectric Capacitor
A capacitor is filled with a dielectric whose dielectric constant varies linearly with distance betw
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
Geometry Effects on Electric Field Distribution
The local electric field strength on a conductor’s surface varies with its curvature. Design an expe
Impact of Conductor Geometry on Shielding Efficiency
A metal enclosure is used for electric shielding but has small apertures in its structure. Evaluate
Impact of Dielectric Constant on Capacitance
The capacitance of a capacitor is influenced by the dielectric constant of the material between its
Impact of Electrode Geometry on Capacitance
An experiment compares the capacitance of a capacitor with differing electrode geometries. The measu
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
Measurement of Electric Field on a Conductor's Surface
A researcher wants to measure the electric field just outside the surface of a spherical conductor.
Measuring the Electric Field of a Conducting Sphere
A researcher is measuring the electric field near the surface of a uniformly charged spherical condu
Method of Images for a Point Charge Near a Conducting Plane
A point charge $$q$$ is placed at a distance $$d$$ above an infinite grounded conducting plane. The
Modeling Electric Field Interactions Between Two Conductors
When two conductors are placed in close proximity, their electric fields interact. Design an experim
RC Circuit Transient Analysis
A capacitor with capacitance $$C$$ is connected in series with a resistor $$R$$ and a constant volta
RC Circuit with Time-Dependent Resistance
In an RC circuit, the resistor is replaced by a time-dependent resistor defined by $$R(t)= R_0*(1+ \
RC Circuit with Time-Dependent Resistance
In a series RC circuit, the resistor's resistance varies with time according to $$R(t)=R_0*(1+\beta*
RC Circuit: Charging and Discharging Analysis with Differential Equations
In an RC circuit, a capacitor charges through a resistor from a DC source. Develop and solve the dif
Superposition of Electric Fields Near a Conductor
A conductor is placed near two point charges. The external charges and the induced charges on the co
Surface Charge Density and Electric Field on a Conductor
Consider a conductor in electrostatic equilibrium. Use Gauss' law to relate the surface charge densi
Temperature Effects on Dielectric Strength
The dielectric constant of a material is temperature-dependent and is given by the relation $$k(T)=
Transient Analysis of a Capacitive Circuit with AC Source
A capacitor in series with a resistor is connected to an AC voltage source given by $$V_{source}(t)=
Transient Discharge of a Capacitor
A capacitor of capacitance $$C$$ is initially charged to a voltage $$V$$ and then allowed to dischar
Tuning Characteristics of a Variable Capacitor in Radio Circuits
Variable capacitors are used in LC circuits for radio tuning. The resonant frequency is given by $$f
AC Circuit Analysis: Impedance in an RLC Series Circuit
An RLC series circuit is used in AC applications. Analyze its impedance and phase characteristics.
AC Circuit Frequency Response with Misapplied Impedance Assumption
A student builds an RLC circuit to investigate its response to an AC voltage source. In the experime
Analysis of a Non-Ideal Battery's Internal Resistance
A battery’s terminal voltage was measured under various load currents to study the effect of interna
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
Battery EMF with Time-Varying Load
A battery with an electromotive force (EMF) of 9 V and an internal resistance of 0.5 Ω is connected
Capacitor Charging Experiment with Time Constant Misinterpretation
In an experiment to study the charging behavior of a capacitor in an RC circuit, a student connects
Capacitors in Parallel: Charge Distribution
Two capacitors, $$C_{1}=4\,\mu F$$ and $$C_{2}=8\,\mu F$$, are connected in parallel to a $$10\,V$$
Derivation of Energy Storage in Capacitors and Inductors
Energy storage in capacitors and inductors is a key concept in circuit theory. Derive the expression
Deriving the Slope of a Power Dissipation Curve
In a laboratory experiment, the power dissipated in a resistor is given by the relation $$P=\frac{V^
Determining Parameters of a Simple Light Circuit
A 60 W incandescent light bulb is rated for 120 V. It can be modeled as a resistor. Answer the follo
Effect of Temperature on Resistor Resistance
A resistor's resistance varies with temperature as $$R(T)=R_0*(1+\alpha*(T-T_0))$$, where $$R_0=50\;
Electrolytic Capacitor Behavior Experiment with Misinterpretation of Dielectric Absorption
An experiment is carried out to measure the charging and discharging curves of an electrolytic capac
Electromotive Force and Internal Resistance Investigations
A battery with an electromotive force (EMF) of 9 V and an internal resistance of 1 \(\Omega\) is con
Energy Analysis of a Constant Power Load in a DC Circuit
A DC circuit supplies a constant power output to a load over a period of time. Analyze the energy de
Energy Efficiency Analysis of Power Supplies
An engineer claims that the energy efficiency of a power supply can be determined by comparing the t
Evaluating Power Factor in an AC Circuit
Measurements were taken in an AC circuit to determine its power factor. The table below includes pha
Experimental Determination of Battery Internal Resistance
A student designs an experiment to determine the internal resistance of a battery. The battery is co
Frequency Dependence of Impedance in a Capacitive Circuit
This question investigates how the impedance of a circuit containing a capacitor changes with freque
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 9: Non-Ideal Battery Analysis
A battery with an electromotive force (EMF) of $$9\,V$$ is connected to an external resistor of $$4\
FRQ 19: Experimental Design: Measuring Capacitance Using an RC Circuit
Design an experiment to measure the capacitance of an unknown capacitor using its charging curve in
Function Generator Misconfiguration in AC Circuit Analysis
An experiment is conducted to study the response of an RLC circuit to an AC signal generated by a fu
Impedance in a Series RLC Circuit
This question involves analyzing the impedance of a series RLC circuit connected to an AC source. Yo
Impedance Measurement in AC Circuits with Ignored Inconsistent Source Behavior
An experiment is conducted to measure the impedance of a complex AC circuit at various frequencies.
Integration Analysis of Variable Resistance in a Non-Uniform Conductor
A non-uniform conductor has a cross-sectional area that varies along its length according to the fun
Investigating Capacitors in Series and Parallel
An experiment was conducted to measure the effective capacitance of two capacitors when connected in
Kirchhoff’s Laws in Multi-loop Circuits
Design a circuit that consists of two loops which share a common resistor. The circuit includes two
Non-Ideal Battery Effects on Circuit Performance
A researcher investigates a circuit in which a battery with EMF E and internal resistance r is conne
Oscilloscope Data Analysis in Circuit Diagnostics
In an electronics lab, an oscilloscope is used to record the voltage waveform across a resistor. The
Oscilloscope Signal Analysis in AC Circuits
An oscilloscope is used to measure the voltage waveform of an AC circuit. The displayed waveform is
Parallel Circuit Analysis and Data Interpretation
Consider a parallel circuit powered by a 12 V battery with two resistors, R1 = 10 Ω and R2 = 20 Ω. A
Power Consumption and Energy Integration in a Circuit
A researcher studies a circuit in which the current varies with time according to $$I(t)=5\cos(0.1*t
Power Variation with Resistance in a Fixed Voltage Circuit
In a circuit with a constant applied voltage, examine how the power dissipated in a resistor changes
RC Circuit Charging and Discharging Analysis
An RC circuit consists of a resistor $$R$$ and a capacitor $$C$$ connected in series with a battery
Series Circuit Analysis using Ohm's Law
Consider a series DC circuit powered by a battery with a constant voltage $$V_0$$. Three resistors a
Series Circuit Analysis with Battery Internal Resistance
A student sets up an experiment in which a battery with an open-circuit electromotive force (EMF) V₀
Series Circuit with Non-Ideal Battery Analysis
Consider a circuit consisting of a non-ideal battery with electromotive force $$\mathcal{E}$$ and in
Series RC Charging Circuit Analysis
A series circuit contains three resistors, R1 = 5 Ω, R2 = 10 Ω, and R3 = 15 Ω, connected in series w
Time-Averaged Power in an AC Circuit
An AC voltage source produces a voltage given by $$V(t)=20\times\cos(100\pi\,t)$$ (in volts) and is
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 in an RL Circuit
Consider an RL circuit where an inductor $$L = 0.5\,H$$ and a resistor $$R = 20\,\Omega$$ are connec
Transient Response in an RL Circuit with Neglected Inductive Kickback Effects
A student investigates the transient response of an RL circuit by abruptly opening a switch and obse
Voltage Divider with Variable Resistor
A voltage divider circuit is built using a fixed resistor and a variable resistor. Investigate how t
Advanced Analysis of Magnetic Interaction in Particle Accelerators
In particle accelerators, charged particles are deflected by magnetic dipole fields. (a) Derive th
Ampère’s Law in a Toroid
A researcher designs a toroid and wishes to determine the magnetic field inside its core. Given the
Analysis of Magnetic Field with Varying Current Density
A long, straight wire does not always carry a uniform current. In a certain experiment, the current
Angular Dependence of Magnetic Force on a Wire
An experiment measured the magnetic force on a current-carrying wire at various angles relative to a
Application of the Biot–Savart Law to a Finite Wire
A finite straight wire carrying a current produces a magnetic field at a point offset from its midpo
Assessing the Accuracy of Magnetic Field Measurements with a Hall Probe Calibration Error
An experiment is conducted to measure the magnetic field of a bar magnet using a Hall probe. The pro
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
Calculus-Based Derivation of Solenoid Magnetic Field using Ampère's Law
A theoretical paper claims to derive the uniform magnetic field inside an ideal solenoid using Ampèr
Comparative Analysis of Magnetic Field Sources
A research laboratory is comparing three different sources of magnetic fields: a solenoid, a circula
Comparison of Magnetic Fields Inside and Outside a Solenoid
Measurements were taken of the magnetic field in and around a long solenoid. The data in the table b
Design Evaluation: Enhancing Electromechanical Systems using Lorentz Force
An industrial design project claims that by optimizing the Lorentz force interaction \(\vec{F} = q\v
Determining the Magnetic Dipole Moment of a Current Loop
A circular current loop of radius 0.08 m carries a current of 7 A. (a) Derive an expression for the
Effect of Number of Turns on a Solenoid's Magnetic Field
In a study of a solenoid's magnetic field, researchers varied the number of turns in the coil while
Experimental Verification of the Biot–Savart Law
An experiment measures the magnetic field at various distances from a long, straight current-carryin
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 Parallel Current-Carrying Wires
Two long, parallel wires carrying currents $$I_1$$ and $$I_2$$ are separated by a distance d. (a)
Force Between Two Parallel Current-Carrying Wires
Two long, parallel wires carry currents I₁ and I₂ and are separated by a distance d. (a) Derive th
Force on a Wire in an External Magnetic Field
Design an experiment to study the force experienced by a current-carrying wire in a uniform external
Investigating Current Density Variation in a Wire with Biot-Savart Law
A detailed study proposes that variations in current density within a non-uniform wire can be modele
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 Magnetic Reversal in a Solenoid via Current Direction Change
A student explores the effect of reversing the current in a solenoid on the direction of its magneti
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 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
Analyze the magnetic field created by a long, straight conductor carrying a steady current. Use Ampè
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 $$J(r)=J_0\le
Magnetic Field in a Toroid
A toroid is a solenoid bent into a circular shape. Consider a toroid with inner radius $$a$$, outer
Magnetic Field Inside a Solenoid
Examine the magnetic field produced inside a solenoid. Derive its theoretical expression and compare
Magnetic Field Inside a Solenoid using Ampère's Law
A long solenoid with a uniform turn density (n turns per unit length) carries a current $$I$$. Using
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 Straight Conductor - Claim Evaluation
A recent popular science article claims that the magnetic field \(B\) around a long, straight curren
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 within a Solenoid
A solenoid 0.50 m in length contains 1000 turns and carries a current of 2.0 A. Using the formula $$
Magnetic Fields Around Conductors
Consider a long, straight current-carrying conductor and a circular current loop lying in the same p
Magnetic Flux through a Non-uniform Loop
A researcher is studying the magnetic flux through a loop that is placed in a spatially varying magn
Measurement of Magnetic Field Gradient Using a Hall Probe
A high-resolution Hall probe is used to measure the magnetic field near a bar magnet by sliding it a
Measurement of Magnetic Field Variation in a Solenoid Under Fixed Current
In this experiment, the magnetic field inside a solenoid is measured at various positions along its
Net Force on a Circular Current Loop in a Non-Uniform Magnetic Field
A circular current loop of radius $$R$$ is placed in a non-uniform magnetic field given by $$B(r)=\f
Non-Uniform Current Density and Magnetic Field Distribution
A recent theoretical investigation claims that for conductors with non-uniform current density, the
Optimization of MRI Magnetic Field Strength
An MRI machine design requires a highly uniform and strong magnetic field, generated by a solenoid.
Superimposed Magnetic Fields from Concentric Loops
Two concentric circular loops with radii $$R_1$$ and $$R_2$$ carry currents $$I_1$$ and $$I_2$$ resp
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 Loop
A rectangular current loop with dimensions a and b carries a current I and is placed in a uniform ma
Torque on a Current Loop in an Electric Motor Design
An engineering report on electric motor efficiency claims that the torque produced by a current loop
Torque on a Current-Carrying Loop
A rectangular current loop is placed in a uniform magnetic field, generating a net torque due to the
Torque on a Twisted Current-Carrying Wire
Design an experiment to measure the torque produced on a twisted current-carrying wire placed in an
Analysis of a Non-Ideal Inductor with Resistive Losses
Consider an inductor with inductance $$L$$ that has a built-in series resistance $$r$$. When a volta
Analysis of an RL Filter Circuit
An RL circuit is used as a low-pass filter. It consists of an inductor L and a resistor R in series
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 Transformer Primary and Secondary Circuits
A transformer has a primary coil with $$N_p$$ turns and a secondary coil with $$N_s$$ turns, with an
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
Applying Gauss's Law in a Symmetric Charge Distribution
Consider a uniformly charged sphere with total charge Q and radius R. (a) Using Gauss’s law, derive
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
Comparative Analysis of LR and RC Circuits
When subjected to a step voltage, both LR and RC circuits exhibit transient responses characterized
Comprehensive Analysis of an RLC Circuit
An RLC circuit consisting of a resistor $$R$$, inductor $$L$$, and capacitor $$C$$ is subjected to a
Damped Oscillations in a Practical LC Circuit
A real LC circuit contains a small resistance R, causing damping of its oscillations. Consider an LC
Deriving Transformer Efficiency via Energy Calculations
A transformer transfers energy from its primary coil to its secondary coil. Assume that the input an
Designing a Magnetic Braking System using Lenz's Law
Engineers are developing a magnetic braking system for high-speed trains utilizing Lenz's law to ind
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 Braking System: Analysis and Design
Electromagnetic braking utilizes Lenz's law where induced currents produce forces that oppose the mo
Electromagnetic Induction Sensor Design
Design a magnetic sensor based on electromagnetic induction that can detect small variations in a ma
Electromagnetic Oscillator Simulation
A circuit is designed incorporating an LC oscillator with a resistor to simulate damping, resulting
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
Experimental Determination of Inductance via Magnetic Field Measurements
In a laboratory experiment, a coil with $$N$$ turns is used to measure the change in magnetic flux $
Experimentally Measuring Magnetic Field Variation
A coil is used to measure the magnetic flux as a magnet is moved relative to it. The following table
Faraday's Law and a Sliding Bar on Rails
A metal bar of length $$l$$ slides on a pair of parallel, conducting rails with a constant velocity
Gauss's Law Application on a Spherical Surface
Consider a spherical Gaussian surface of radius R centered on a point charge Q. Answer the following
Generator Operation and Induction Heating Comparison
Electromagnetic induction is the principle behind both electrical generators and induction heating d
Induced EMF in a Rotating Loop
A rectangular loop of area $$A$$ rotates with constant angular velocity $$\omega$$ in a uniform magn
Induction Coil Experiment and Lenz’s Law
In an experiment, a rectangular coil is rapidly inserted into a solenoid connected to a galvanometer
Induction Cooktop Energy Transfer Analysis
A researcher examines the efficiency of an induction cooktop by measuring the rate of temperature in
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
Induction Heating: Experimental Design and Analysis
Induction heating uses electromagnetic induction to heat conductive materials. Design an experiment
Inductive Kickback and Energy Dissipation in an R-L Circuit
A researcher studies the phenomenon of inductive kickback in an R-L circuit when the current is sudd
Inductive Response in a Spatially Non-Uniform Magnetic Field
A single rectangular loop of wire (dimensions: 0.2 m by 0.3 m) is placed in a magnetic field that va
Inductor Energy Storage and Discharge
An inductor with inductance $$L$$ carries a steady current $$I$$, thereby storing magnetic energy in
LC Circuit Resonance Analysis
An LC circuit oscillates due to the energy exchange between an inductor (with inductance $$L$$) and
LR Circuit Transient Analysis
Consider an LR circuit with a resistor of resistance $$R$$ and an inductor of inductance $$L$$ conne
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
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
Non-uniform Magnetic Field and Loop Induction
This problem deals with the induction of EMF in a rectangular loop entering a region where the magne
Optimizing Generator Output via Angular Velocity Variation
A wind turbine generator rotates a coil in a magnetic field, and a researcher varies the angular vel
Resonant Frequency Sensitivity of LC Circuit
The resonant frequency of an LC circuit is given by $$f = \frac{1}{2\pi\sqrt{L*C}}$$. Analyze the se
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
Sensitivity of Resonant Frequency to Component Changes in an LC Circuit
The resonant frequency of an LC circuit is given by $$f = \frac{1}{2\pi\sqrt{L*C}}$$.
Stationary Loop in a Time-Varying Magnetic Field
A stationary square loop with side length $$L$$ is placed in a region where the magnetic field varie
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 Behavior and Efficiency
A transformer has a primary coil with $$N_p$$ turns and a secondary coil with $$N_s$$ turns. An alte
Transformer Efficiency Analysis
A transformer is used to step down a primary voltage of $$240\,V$$ to a secondary voltage of $$24\,V
Transient Response in an LR Circuit
An LR circuit consists of a resistor $$R = 10$$ Ω and an inductor $$L = 2$$ H. A step voltage of 20
Transient Response in an RL Circuit with Time-Varying Resistance
Consider an RL circuit where the resistor's value varies with time as $$R(t) = R_0 (1 + \alpha*t)$$,
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
Variable Capacitance in an LC Circuit: Resonant Frequency Analysis
In an LC circuit, suppose the capacitance varies with time as C(t) = C₀*(1 + α*t), where α is a smal
Wireless Power Transfer and Inductive Coupling Analysis
In a wireless power transfer system, two coils are used for energy transfer. Assume the primary coil
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.
Browse top AP materials
We’ve found the best flashcards & notes on Knowt.
Explore top AP flashcards
Flashcards (30)Explore top AP notes
Note Tips from Former AP Students
FAQ
We thought you might have some questions...
- 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.