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.
Analyzing Electric Field Lines and Charge Distributions
Electric field lines provide a visual representation of the field. Analyze the principles behind the
Calibrating an Electroscope: Charging and Discharging Phenomena
Design an experiment to calibrate an electroscope by studying its charging and discharging behavior.
Charge Interaction in Mixed Media
A computer simulation investigates how two point charges interact when placed in media with differen
Charge Redistribution in Connected Conductors
Two conducting spheres with radii R₁ and R₂, initially carrying charges Q₁ and Q₂ respectively, are
Comparative Analysis of Electric Potential on Varying Geometries Using Gauss's Law
Design an experiment to compare the electric potential distributions for different charge geometries
Coulomb's Law Experiment with Isolated Charges
In this experiment, an experimenter uses two small insulating spheres, each with a known discrete ch
Coulomb's Law: Force Gradient Analysis
Two charged particles with charges q₁ and q₂ interact in a vacuum. The force between them is given b
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 from a Uniformly Charged Plane
An infinite plane sheet with uniform surface charge density produces a constant electric field. Anal
Electric Field from an Extended Linear Charge Distribution
A thin rod of length $$L = 0.50 \; m$$ has a uniform linear charge density $$\lambda = 2.0*10^{-8} \
Electric Field Lines and Charge Distribution Analysis
This problem explores the properties of electric field lines for a dipole and requires both qualitat
Electric Field of a Charged Cylinder
A long cylindrical rod of radius $$R = 0.05 \; m$$ has a uniform volume charge density of $$\rho = 4
Electric Field of a Planar Charge Distribution and Edge Effects
A researcher analyzes the electric field produced by a uniformly charged infinite plane and compares
Electric Field of a Uniformly Charged Sphere Using Gauss's Law
This problem involves applying Gauss's law to determine the electric field produced by a uniformly c
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 Curved Surface in a Non-uniform Field
Consider an electric field that varies with the y-coordinate according to $$E(y) = k * y$$, where th
Electric Potential Energy of a Continuous Charge Distribution
A researcher seeks to determine the total electric potential energy stored in a continuous charge di
Electric Potential from a Point Charge
A point charge $$Q = +3.0*10^{-9} \; C$$ is located at the origin. Answer the following:
Electric Potential from a Uniformly Charged Rod
This problem requires you to derive the electric potential at a point on the perpendicular bisector
Electrostatic Induction and the Faraday Cage
A researcher is exploring electrostatic induction and the effectiveness of a Faraday cage in shieldi
Electrostatic Shielding Experiment
An experiment is set up to investigate how a conducting shell can shield its interior from external
Experiment to Determine the Permittivity of Free Space with Parallel Plates
Design an experiment using a parallel plate capacitor to determine the permittivity of free space, $
FRQ 2: Electric Field Measurement around a Uniformly Charged Sphere
A report claims that the electric field measured outside a uniformly charged sphere obeys the relati
FRQ 4: Analysis of Non-Uniform Electric Field in a Laboratory Setup
A student reports that their electric field measurements in a region with multiple charge sources sh
FRQ 10: Critical Analysis of Electric Potential Gradient Study
A study claims that a constant spatial gradient in electric potential was measured across a complex
FRQ 13: Reconstructing Gauss' Law for a Cylindrical Charge Distribution
A research paper claims that by applying Gauss' law to a cylindrical charge distribution, one can de
FRQ 19: Evaluation of Electric Field Line Distribution Claims
A recent report suggests that the density of electric field lines in simulation images accurately re
Gauss’s Law in a Uniformly Charged Sphere
A non‐conducting sphere of radius R = 0.5 m carries a uniformly distributed charge Q = 1.0×10⁻⁶ C. U
Graph Analysis of Electric Potential vs. Distance
The electric potential due to a point charge is given by $$V(r) = \frac{kq}{r}$$. Analyze how the th
Mapping Electric Field Intensity Through Probe Measurements
A laboratory experiment is performed in which a probe is used to measure the electric field strength
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
Mapping the Electric Field of a Charged Sphere
Design an experiment to map the electric field around a uniformly charged insulating sphere using a
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
Point Charge Potential Calculation
Consider a point charge of $$Q = 4.00 \; \mu C$$. (a) Derive the expression for the electric potent
Superposition of Electric Fields in a Composite System
A composite electrical system consists of a point charge and an extended charge distribution. A poin
Superposition of Electric Potentials
This problem involves calculating the net electric potential at a point due to two point charges usi
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
Voltage Differences in Resistive Circuits and Electric Potentials
In a resistive circuit, the voltage at several nodes was measured. Use the data provided to analyze
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 Done on a Test Charge from Discrete Electric Field Data
A test charge is moved along a straight path in a non-uniform electric field. The measured electric
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$$ are connected
Analyzing Charge Distribution on a Composite Conductor
A researcher explores a composite conductor comprising regions with different curvatures and materia
Analyzing Gradual Dielectric Insertion in a Capacitor
Gradually inserting a dielectric material into a capacitor can continuously change its capacitance.
Calculus Analysis of Electric Field and Potential in a Non-Uniform Capacitor
A parallel plate capacitor contains a non-uniform dielectric where the permittivity varies with dist
Calculus Derivation of Electric Field Around a Charged Cylindrical Conductor
A long cylindrical conductor carries a non-uniform surface charge density given by $$\sigma(z)=\sigm
Capacitor Charging and Discharging in an RC Circuit
In a series RC circuit, a capacitor with capacitance \(C\) is charged by a constant voltage source \
Capacitor Charging in an RC Circuit with Constant Resistance
A capacitor with capacitance $$C$$ is connected in series with a resistor of resistance $$R$$ and a
Capacitor Discharge Curve and Time Constant Computation
A capacitor in an RC circuit discharges over time, and its voltage follows the equation $$V(t)=V_0 e
Derivation of Capacitance Change Due to Temperature-Dependent Dielectric
The dielectric constant of a capacitor material is temperature-dependent, given by $$k(T)=k_i+\delta
Design and Analysis of a Faraday Cage
A researcher is designing a Faraday cage to shield sensitive electronic equipment from external elec
Design of a Dual-Capacitor System for Peak Power Applications
A research team is designing a system using dual capacitors configured in series and parallel to opt
Designing a Faraday Cage for Sensitive Instrumentation
A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo
Effect of Dielectrics on Capacitance
A capacitor initially in vacuum with capacitance $$C_0$$ has a dielectric material with dielectric c
Effect of Dielectrics on Capacitance: A Comparative Study
A researcher investigates the effect of different dielectric materials on the capacitance of a paral
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 and Faraday Cage Effectiveness
A research laboratory is designing a Faraday cage to protect sensitive equipment from external elect
Electric Shielding Effectiveness Experiment
In an experiment designed to evaluate the effectiveness of electric shielding by a Faraday cage, a r
Electrostatic Analysis of an Irregular Conductor
An irregularly shaped conductor carries a net charge $$Q$$. Due to its geometry, some regions have h
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 Dissipation During Capacitor Discharge
When a capacitor discharges through a resistor, energy is dissipated as heat. Design an experiment t
Energy Loss Due to Dielectric Heating in AC Capacitor Circuit
In an AC circuit containing a capacitor with a dielectric, experimental data were collected to measu
Energy Storage in a Parallel Plate Capacitor with Dielectric Investigation
A parallel plate capacitor with inserted dielectric is examined to understand how the energy stored
Energy Stored in a Parallel Plate Capacitor - Calculus Based Derivation
A parallel plate capacitor with plate area \(A\) and plate separation \(d\) is filled with a dielect
Experimental Analysis of Dielectric Breakdown
A researcher investigates the dielectric strength of several insulating materials. The experiment in
FRQ 1: Electrostatic Equilibrium in Conducting Spheres
In this experiment, a uniformly charged metal sphere is allowed to reach electrostatic equilibrium.
FRQ 2: Effectiveness of a Faraday Cage in Electric Shielding
A researcher builds a Faraday cage of various metal thicknesses and monitors the internal electric f
FRQ 2: Electric Shielding in a Sensor Enclosure
Sensitive biomedical sensors are enclosed in a metal box to protect them from external electromagnet
FRQ 7: Capacitor Discharge with a Time-Dependent Resistor
In an experimental circuit, a capacitor of capacitance $$C$$ is discharged through a resistor whose
FRQ 9: Comparative Analysis of Capacitive Energy Storage
Two identical capacitors are connected in two different configurations: one in series and the other
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: Energy Storage in Capacitors Under Varying Voltages
An experiment is performed in which the energy stored in a capacitor is measured at different applie
FRQ 13: Theoretical Analysis of Electric Field Shielding in Layered Conductors
Multiple concentric conductive shells are used to shield a sensitive instrument from external electr
FRQ 17: Optimization of Capacitor Design for Maximum Energy Density
A company is designing a parallel plate capacitor for high-energy storage applications. The energy s
Impact of Dielectric Constant on Capacitance
The capacitance of a capacitor is influenced by the dielectric constant of the material between its
Investigating the Role of Curvature on Surface Charge Density in Conductors
A researcher studies a set of conductors with different curvatures (from flat plates to spheres) and
Optimizing Conductive Coatings for Electric Shielding
Different conductive coatings can affect the effectiveness of electric shielding. Design an experime
Parallel Plate Capacitor: Effect of Dielectric Insertion
A parallel plate capacitor initially charged to a voltage $$V$$ is modified by the slow insertion of
RC Circuit Capacitor Charging Analysis
Consider an RC circuit where a capacitor is charged by a constant voltage source. A researcher claim
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 Redistribution on Irregularly Shaped Conductors
An irregularly shaped conductor has varying curvature along its surface, leading to a non-uniform su
Transient Analysis of a Capacitor with a Time-Varying Voltage Source
A capacitor is connected to a voltage source whose output is sinusoidal, given by $$V(t)=V_0 \sin(\o
AC Circuit Analysis: Impedance in an RLC Series Circuit
An RLC series circuit is used in AC applications. Analyze its impedance and phase characteristics.
AC Circuit: Impedance and Power Factor Analysis
An AC circuit operates at a frequency of $$f = 60$$ Hz and consists of a resistor (R = $$10$$ $$\Ome
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 Measurement Uncertainty in Circuit Diagnostics
A technician using a digital multimeter reports highly consistent current measurements in a circuit.
Analyzing RC Filter Behavior
An RC low-pass filter is constructed with $$R = 1\,k\Omega$$ and $$C = 1\,\mu F$$. The input voltage
Analyzing Temperature Effects on a Thermistor in a Circuit
A thermistor is used in a sensing circuit, and its resistance varies with temperature. The table bel
Capacitance in Complex Networks
In a circuit containing both series and parallel capacitors, a claim is made that the total capacita
Capacitor Charging Diagram Analysis
A graph is provided that represents the capacitor charging process in an RC circuit. Analyze the dia
Charging a Capacitor in an RC Circuit
A capacitor is connected in series with a resistor and a DC voltage source. Using calculus, derive a
Circuit Design Challenge: Maximizing Power Transfer
A circuit is designed to maximize power transfer to a load resistor. Using the Thevenin equivalent c
Custom RC Filter Experimental Analysis with Ignored Loading Effect
An experiment is performed to characterize the frequency response of a custom-built RC low-pass filt
Deriving the Slope of a Power Dissipation Curve
In a laboratory experiment, the power dissipated in a resistor is given by the relation $$P=\frac{V^
Design and Analysis of an RC High-Pass Filter
A researcher designs an RC high-pass filter using a resistor of $$R=2000\,\Omega$$ and a capacitor o
Design of a Low-Pass RC Filter
Design a low-pass RC filter to attenuate frequencies above 1 kHz. (a) Starting from the voltage divi
Energy Delivered by a Time-Varying Power Source
A circuit delivers power according to $$P(t)=100*e^{-0.5*t}$$ Watts. (a) Set up and evaluate the int
Energy Storage in a Capacitor
A capacitor with capacitance \(C = 100\,\mu F\) is charged to a voltage of \(50\,V\).
Evaluating Measurement Errors in Circuit Instruments
Measurement errors in electrical instruments can propagate through calculations. Evaluate the error
Frequency Dependence of Impedance in a Capacitive Circuit
This question investigates how the impedance of a circuit containing a capacitor changes with freque
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 16: Circuit Measurement Techniques
In a laboratory setting, students are asked to measure voltage, current, and resistance in a circuit
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
Impact of Capacitance on RC Circuit Time Constant
This question focuses on the effect of capacitance on the RC time constant, integrating both theoret
Impact of Temperature on Resistance
Resistance in a conductor can change with temperature. Investigate this variation and its implicatio
Impedance Variation with Frequency in a Series RLC Circuit
A researcher investigates the impedance of a series circuit containing a resistor, an inductor, and
Investigating Capacitors in Series and Parallel
An experiment was conducted to measure the effective capacitance of two capacitors when connected in
Kirchhoff’s Current Law in a Multi-Branch Circuit
In an experimental setup, measurements at a node show two currents entering as \(I_1 = 2.5\,A\) and
Kirchhoff's Voltage Law in a Multi-Loop Circuit
A multi-loop circuit contains a 15 V battery and three resistors with values R1 = 3 Ω, R2 = 4 Ω, and
Measuring Circuit Parameters with Multimeter and Oscilloscope
A technician uses a multimeter and an oscilloscope to determine various circuit parameters. Analyze
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
Parallel Circuit Analysis with Exponential Resistance Change
A researcher investigates a parallel circuit where three branches contain resistors whose resistance
Parallel Circuit and Power Dissipation Calculation
A parallel circuit is constructed with two branches: in branch 1, a resistor of R1 = 8 Ω is connecte
Power Calculation from Voltage and Current Data
A set of voltage and current measurements were taken from an electrical circuit during an experiment
Power Dissipation Analysis in a Resistor
In a resistor with \(R = 8\,\Omega\), the current is time-dependent and given by the function $$I(t)
Power Dissipation and Energy in a Resistive Circuit
A resistive circuit is powered by a constant current source. Examine the energy transfer in the resi
Power Variation with Resistance in a Fixed Voltage Circuit
In a circuit with a constant applied voltage, examine how the power dissipated in a resistor changes
RC Low-Pass Filter Frequency Response Analysis
A research group hypothesizes that an RC low-pass filter attenuates high-frequency signals such that
Resistance Measurements and Conductor Geometry
A uniform wire with a length L = 2 m and cross-sectional area A = 1 mm² (1×10⁻⁶ m²) is made of a mat
Series Circuit Analysis using Ohm's Law
Consider a series DC circuit powered by a battery with a constant voltage $$V_0$$. Three resistors a
Temperature Effects on Conductor Resistance and Circuit Current
A researcher studies how temperature affects the resistance of a conductor. The resistance is given
Temperature Effects on Resistance in a Voltage Divider
A thermistor with a resistance that varies with temperature according to $$R(T)=R_0(1+\alpha T)$$, w
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 After a Switch is Closed
An RL circuit is energized by closing a switch to connect a DC voltage source. Analyze the transient
Transient Response of an RC Circuit
An RC circuit with a resistor \(R = 10\,\Omega\) and a capacitor \(C = 2\times10^{-3}\,F\) is connec
Voltage Divider Design and Power Efficiency Analysis
Design a voltage divider circuit that outputs 5 V from a 12 V supply. Analyze its performance, parti
Voltage Divider with Variable Resistor
A voltage divider circuit is built using a fixed resistor and a variable resistor. Investigate how t
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 Flux in a Rotating Loop
A single-turn loop of area A is rotating in a uniform magnetic field of strength B with a constant a
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
Analyzing the Effectiveness of an Electromagnet Design
An electromagnet is made by wrapping a coil around a ferromagnetic core. (a) Derive an expression
Axial Magnetic Field of a Bar Magnet
Model a bar magnet as a magnetic dipole and derive an expression for the magnetic field along its ax
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
Charged Particle in Combined Electric and Magnetic Fields
In a complex experimental setup, a charged particle is exposed simultaneously to a uniform electric
Critical Analysis of Ampère's Law in a Non-Uniform Magnetic Field
An experiment uses a loop to measure the magnetic field in a region where the field is non-uniform.
Current Variation and Magnetic Field Strength
In an experiment, the magnetic field is measured at a fixed distance from a straight conductor while
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
Determining Torsional Stiffness from Experimental Data
In an experiment, a wire is twisted and the applied torque and corresponding angle of twist are reco
Determining Torsional Stiffness of a Twisted Wire
A wire is twisted by applying a torque, leading to an angular displacement. The relation is given by
Effect of Loop Area on Solenoid Magnetic Field
In an experimental study, a researcher examines how the area of a loop placed inside a solenoid affe
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
A current-carrying wire oriented at different angles relative to a uniform magnetic field experience
Experimental Analysis of Magnetic Field Variation with Distance
In an experiment, the magnetic field around a long, straight conductor was measured at different dis
Experimental Determination of the Magnetic Moment of a Bar Magnet
A student seeks to determine the magnetic moment of a bar magnet by measuring the deflection of a co
Experimental Verification of the Right-Hand Rule
A recent experimental study claims that the right-hand rule always accurately predicts the direction
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 parallel wires, each carrying a current of 5 A, experience a mutual force of attraction. Data we
Force Between Two Parallel Current-Carrying Wires
Two long, parallel wires are separated by 5 cm. Wire 1 carries a current of 6 A and Wire 2 carries 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 Current-Carrying Wire at an Angle in a Magnetic Field
A 0.30 m long straight wire carrying a current of 5.0 A is placed in a uniform magnetic field of 0.2
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 Curved Current-Carrying Arc
A curved wire in the shape of an arc with radius R and central angle $$\phi$$ carries a current I an
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
Induced EMF and Changing Magnetic Flux in a Rotating Loop
A rectangular loop with an area of $$A = 0.05\,m^2$$ rotates in a uniform magnetic field of 0.1 T at
Induced EMF in a Rotating Loop
A rectangular loop of area $$A$$ rotates with a constant angular velocity $$\omega$$ in a uniform ma
Interaction of Magnetic and Electric Fields in a Particle Detector
In a particle detector, charged particles traverse a region where both electric and magnetic fields
Lorentz Force on a Moving Particle in Combined Fields
A particle with charge $$q = 1.0 \times 10^{-6} \text{ C}$$ moves with a velocity of $$v = 3.0 \time
Magnetic Dipole-Dipole Interaction Energy
Consider two magnetic dipoles, each with magnetic moment $$m$$, separated by a distance $$d$$. Using
Magnetic Field from a Straight Conductor
A long, straight conductor carries a constant current. Using the formula $$B = \frac{\mu_0 * I}{2\pi
Magnetic Field from a Wire with Variable Current Distribution
A current-carrying wire has a linear current distribution along its length described by $$\lambda(x)
Magnetic Field in a Toroid
A toroid with N turns is used to study the magnetic field inside it. The field is theoretically give
Magnetic Field Inside a Solenoid
A solenoid has a length of 0.50 m, 500 turns, and carries a current of 2 A. (a) Use Ampère's Law to
Magnetic Field Inside a Toroid
A toroid with N turns carrying a current I has a mean radius R. (a) Derive the expression for the
Magnetic Field Mapping around a Straight Conductor
An experiment was conducted to measure the magnetic field produced by a straight current-carrying co
Magnetic Field Mapping of a Bar Magnet
A researcher collects experimental data measuring the magnetic field strength at various distances f
Magnetic Field of a Bar Magnet
A bar magnet has a north and a south pole and produces a dipolar magnetic field. (a) Describe qual
Magnetic Field of a Circular Current Loop
An experimental setup consists of a single circular loop of wire carrying a steady current of 5 A. T
Magnetic Field of a Finite Length Wire Using Biot–Savart Law
A finite straight wire of length $$L = 0.3\,m$$ carries a current of 5 A. The wire is oriented along
Magnetic Field of a Long Straight Conductor
A power company uses long, straight conductors to transmit electrical power. In one section of the s
Magnetic Field of a Straight Conductor
Consider a long, straight conductor carrying a constant current I. Using Ampère's Law, derive the ex
Magnetic Field of a Straight Conductor
A long, straight wire carries a steady current. Using Ampère's law, derive the expression for the ma
Magnetic Force on a Moving Charged Particle
In a controlled laboratory experiment, a charged particle with charge $$q = 2\times10^{-6} \; C$$ an
Mapping Magnetic Field Directions in a Multi-Wire Assembly
A factory assembly involves multiple wires carrying currents in different directions arranged perpen
Measurement of Magnetic Field Gradient Using a Hall Probe
A high-resolution Hall probe is used to measure the magnetic field near a bar magnet by sliding it a
Motion of a Charged Particle in Combined Electric and Magnetic Fields
A charged particle enters a region with both a uniform electric field (directed upward) and a unifor
Oscillatory Motion of a Current Loop in a Magnetic Field
A rectangular current loop suspended in a uniform magnetic field experiences a torque which causes i
Superimposed Magnetic Fields from Concentric Loops
Two concentric circular loops with radii $$R_1$$ and $$R_2$$ carry currents $$I_1$$ and $$I_2$$ resp
Superposition of Magnetic Fields from Multiple Coils
An array of N identical circular coils (each with radius R and carrying current I) is arranged along
Torque on a Current Loop
A square current loop of side length \(a\) is placed in a uniform magnetic field \(B\) such that the
Torque on a Current Loop
A rectangular loop carrying a current is placed in a uniform magnetic field. (a) Derive an express
Torque on a Current Loop in a Magnetic Field
A square current-carrying loop with side length $$L$$ is placed in a uniform magnetic field $$B$$. T
Uniform Magnetic Field in a Solenoid
A researcher builds a solenoid to investigate how the magnetic field inside is affected by the numbe
Verification of Ampère's Law in a Laboratory Setting
A laboratory report claims that Ampère's Law \(\oint \vec{B} \cdot d\vec{l} = \mu_0 * I_{enc}\) hold
Verification of the Biot–Savart Law
Design an experiment to verify the Biot–Savart Law by mapping the magnetic field produced by a small
Ampere's Law and Displacement Current
In a charging capacitor, the changing electric field between the plates necessitates the use of Ampe
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 Back EMF in an Electric Motor
After an electric motor is turned off, its collapsing magnetic field induces a back EMF. A researche
Analysis of Gauss's Law using a Spherical Charge Distribution
This problem applies Gauss's Law to calculate the electric field outside a uniformly charged sphere.
Analysis of Inductance in Coiled Materials
A set of coils with identical geometry are constructed using different core materials. The table bel
Analysis of LR Circuit Behavior Using Calculus
Consider an LR circuit consisting of a resistor $$R$$ and an inductor $$L$$ connected in series to a
Analyzing Transformer Coupling and Mutual Inductance
A transformer consists of two coils with primary turns $$N_1$$ and secondary turns $$N_2$$. The coup
Application of Ampere's Law with Maxwell Correction in a Capacitor System
This problem applies Ampere's Law with Maxwell's correction to analyze the displacement current in a
Application of Faraday's and Lenz's Laws in an Induction Cooktop
An induction cooktop heats a metal pot by using a coil that produces a rapidly alternating magnetic
Application of Maxwell's Equations in Field Analysis
A researcher uses Maxwell's equations to analyze a laboratory setup involving both electric and magn
Comparative Analysis of LR and RC Circuits
When subjected to a step voltage, both LR and RC circuits exhibit transient responses characterized
Coupled Inductors and Mutual Inductance in Transformers
A researcher examines a transformer system with two coupled inductors to study mutual inductance and
Deriving Transformer Efficiency via Energy Calculations
A transformer transfers energy from its primary coil to its secondary coil. Assume that the input an
Designing an Experiment to Verify Lenz's Law
Lenz’s law states that the direction of the induced current in a conductor due to a changing magneti
Effect of Coil Turns on Induced EMF
A researcher varies the number of turns in a coil while keeping the rate of change of magnetic flux
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
Experimental Determination of Inductance
In an experiment, a student studies an LR circuit by measuring the current rise after closing a swit
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
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
Gauss's Law for Magnetic Fields
Gauss's Law for magnetic fields indicates that the net magnetic flux through any closed surface is z
Gauss's Law for Magnetic Fields: A Theoretical Examination
Consider a closed, irregularly shaped surface placed in a uniform magnetic field. Address the follow
Graphical Analysis of Magnetic Flux Variation
The graph provided shows the measured magnetic flux through a loop as a function of time. Using the
Induced EMF in a Time-Varying Solenoid
Consider a long solenoid with $$N$$ turns, radius $$r$$, and a uniform magnetic field inside that is
Induction Cooktop Energy Transfer Analysis
A researcher examines the efficiency of an induction cooktop by measuring the rate of temperature in
Induction Heating Analysis
Induction heating utilizes induced eddy currents to heat metal objects. Consider an experiment where
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
Induction heating devices heat metal objects by inducing eddy currents within them. The efficiency o
Induction Heating: Experimental Design and Analysis
Induction heating uses electromagnetic induction to heat conductive materials. Design an experiment
Induction in a Solenoid with Time-Varying Magnetic Field
A solenoid with 200 turns, length 0.5 m, and cross-sectional area 0.01 m² is subjected to a time-var
Investigating Induced EMF in a Rotating Loop
A conducting loop of area $$A$$ rotates in a uniform magnetic field $$B$$ with constant angular velo
LC Circuit Oscillations
An LC circuit is composed of an inductor $$L$$ and a capacitor $$C$$. When the circuit is closed, en
LR Circuit Analysis and Energy Storage
An LR circuit consists of a resistor (R = 5 Ω) and an inductor (L = 0.1 H) connected in series. A co
LR Circuit Transient Response
Consider an LR circuit comprising an inductor with inductance $$L$$ and a resistor of resistance $$R
Magnetic Field in a Toroid via Ampere's Law
Consider a toroid with $$N$$ turns and a mean radius $$r$$. Use Ampere's law to determine the magnet
Magnetic Flux Measurement Using a Hall Sensor
A Hall sensor is used to measure the magnetic flux through a loop as it rotates in a uniform magneti
Magnetic Flux Variation in a Moving Loop
A square loop with side length 0.20 m moves with a constant velocity of 3 m/s from a region with zer
Magnetic Levitation and Electromagnetic Braking
Magnetic levitation (maglev) trains use electromagnetic induction both to levitate above the tracks
Magnetic Levitation Experiment Using Eddy Currents
In an experiment aimed at achieving magnetic levitation, a magnet is suspended over a conductive pla
Maxwell's Correction in a Charging Capacitor Circuit
In a parallel-plate capacitor being charged by a constant current, the electric field between the pl
Oscillations in a Series LC Circuit
A series LC circuit is built with an inductor of L = 0.5 H and a capacitor of C = 200 μF (200×10⁻⁶ F
Oscillations in an LC Circuit
An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.
Propagation of Electromagnetic Waves via Maxwell's Equations
Electromagnetic waves in a vacuum are governed by Maxwell's equations. Answer the following:
Resonant Frequency Variation in an LC Circuit
An LC circuit consists of an inductor with inductance $$L$$ and a variable capacitor with capacitanc
Rotating Generator Experiment
In an experiment designed to analyze the output of a rotating generator, a coil connected to a voltm
Rotating Loop EMF Analysis
Consider a rectangular conducting loop of area $$A$$ rotating in a uniform magnetic field $$B$$ with
Rotating Loop in a Magnetic Field
A single-loop coil of area $$A$$ rotates with a constant angular velocity $$\omega$$ in a uniform ma
Sensitivity of Resonant Frequency to Component Changes in an LC Circuit
The resonant frequency of an LC circuit is given by $$f = \frac{1}{2\pi\sqrt{L*C}}$$.
Stationary Loop in a Time-Varying Magnetic Field
A stationary square loop with side length $$L$$ is placed in a region where the magnetic field varie
Transformer Design and Analysis
A transformer is designed to step down an input voltage $$V_{p}$$ to an output voltage $$V_{s}$$. Th
Transformer Efficiency Experiment with Core Saturation
A laboratory experiment is set up to study voltage transformation in a step-down transformer. The pr
Transformer Voltage Ratio and Efficiency
A transformer is built with a primary coil of N₁ = 500 turns and a secondary coil of N₂ = 50 turns.
Transient Analysis in an LR Circuit
An LR circuit consists of an inductor with $$L=2\;H$$ and a resistor with $$R=4\;\Omega$$ connected
Transient Behavior Analysis in an LR Circuit
A researcher examines the transient current behavior in an LR circuit immediately after the switch i
Transient LR Circuit Response
A series LR circuit is connected to a battery at $$t = 0$$, and the current begins to rise exponenti
Transient Response in an LR Circuit
Consider an LR circuit consisting of an inductor $$L$$ and a resistor $$R_{loop}$$ connected in seri
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
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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.