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.
Analyzing Electric Field Lines and Charge Distributions
Electric field lines provide a visual representation of the field. Analyze the principles behind the
Applying Gauss' Law for a Spherical Conductor
In a lab experiment, the electric flux through spherical surfaces of various radii is measured aroun
Calculating the Electric Field of a Cylindrical Charge Distribution
A simulation experiment is conducted to measure the electric field around a long, uniformly charged
Calculating Work Done by an Electric Field in Moving a Particle
In this problem you will calculate the work done by an electric field on a charged particle moving b
Calibrating an Electroscope: Charging and Discharging Phenomena
Design an experiment to calibrate an electroscope by studying its charging and discharging behavior.
Capacitor with Dielectric Insertion
This problem examines how the capacitance and stored energy of a parallel plate capacitor change whe
Charge Conservation and Circuit Analysis in a Complex System
This problem integrates the principles of charge conservation within a circuit. You will first discu
Charge Conservation and Electrostatic Interactions
Charge conservation and electrostatic interactions are fundamental concepts in electromagnetism. Dis
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
Charge Redistribution in Connected Conductors
Two conducting spheres with radii R₁ and R₂, initially carrying charges Q₁ and Q₂ respectively, are
Charging and Discharging of a Capacitor: Calculus Approach
In this question, you will derive and solve the differential equation governing the charging/dischar
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
Data Analysis of Electric Force Measurements
In a laboratory experiment, the force between charged spheres was measured at various distances. Usi
Determining Surface Charge Density on a Conductor
An experiment is conducted to determine the surface charge density on a conductor by measuring the e
Dipole in a Non-Uniform Electric Field: Torque and Equilibrium
A dipole with moment p is placed in a non-uniform electric field given by $$E(x)= E₀*(1+β*x)$$. Usin
Effect of Dielectric on a Parallel-Plate Capacitor
A parallel-plate capacitor with plate area A and separation d is partially filled with a dielectric
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 Dipole Potential
An electric dipole consists of charges $$+q$$ and $$-q$$ separated by a distance $$d = 0.05 \; m$$,
Electric Field Due to a Point Charge
A point charge of $$+2.0*10^{-9} \; C$$ is located at the origin in a vacuum. Answer the following:
Electric Field Due to a Uniformly Charged Sphere
In this problem you will derive the electric field expressions for points both outside and inside a
Electric Field from a Cylindrical Charge Distribution
An infinitely long cylindrical rod of radius $$R = 0.05 \; m$$ carries a uniform volume charge densi
Electric Field in a Cylindrical Charge Distribution
This problem involves using Gauss's law to analyze a cylindrical charge distribution. Provide detail
Electric Fields in Multi-layer Media: Conductors and Insulators
A layered system consists of a conductor and an insulator in contact. Analyze the electric field dis
Electric Potential and Field from a Point Charge
A point charge of 5 μC is located at the origin. (a) Write the expression for the electric potential
Electric Potential and Work in a Particle Accelerator Setup
In a particle accelerator experiment, the electric potential difference along the acceleration path
Electric Potential Energy in a System of Charges
Consider a system of point charges. Explore the concept of electric potential energy within this sys
Electric Potential Energy in a Three-Charge System
Three point charges, q₁, q₂, and q₃, are placed at the vertices of an equilateral triangle with side
Electric Potential Energy of a Uniformly Charged Rod
Derive an expression for the electric potential energy stored in a uniformly charged rod and discuss
Electric Potential Landscape of a Dipole
A simulation experiment maps the electric potential in the region around an electric dipole. The set
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
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, $
Exploring Gauss' Law in a Multi-Charged Environment
Students design an experiment in which multiple point charges are arranged inside a closed surface.
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 6: Integration for Electric Potential from a Continuous Charge Distribution
A recent study claims that the electric potential produced by a non-uniform line charge can be expre
FRQ 12: Evaluating Electric Potential Energy Change in a Particle Accelerator
A research article claims that measured changes in the electric potential energy of particles in an
Gauss' Law for a Non-Uniform Spherical Charge Distribution
Consider a sphere of radius R with a radial dependent charge density given by $$\rho(r) = \rho_0*(r/
Gauss' Law: Spherical Charge Distribution
A point charge is enclosed within a spherical surface. Analyze the electric flux through the sphere
Gauss's Law Applied to an Infinite Sheet
Apply Gauss's law to derive and analyze the electric field of an infinite plane sheet of charge. Res
Gaussian Surface and Electric Flux for a Point Charge
A point charge of $$+2.0*10^{-9} \; C$$ is positioned at the center of a spherical Gaussian surface
Integration to Determine Electric Potential along a Line
A uniformly charged rod creates an electric potential along its axis. Determine this potential using
Investigating the Relationship between Electric Flux and Surface Geometry
A simulation is designed to explore how electric flux through a surface depends on the geometry of t
Mapping Electric Field in a Complex Geometry via Monte Carlo Integration
An experiment is performed to map the electric field in a region with a complex charge distribution
Motion of a Charged Particle in a Uniform Electric Field
A charged particle is released from rest in a uniform electric field. Analyze its motion using calcu
Path Integral for Work in a Non-Uniform Electric Field
A charged particle moves in a non-uniform electric field given by $$E(x,y) = (A*x, B*y)$$. The parti
Point Charge Interaction Experiment
Two point charges are fixed in space, and an experiment is carried out to measure the force experien
Point Charge Interactions and Coulomb's Law
Two point charges are placed along the x-axis in a vacuum. Let $$q_1 = +1.602*10^{-19} \; C$$ be loc
Potential from a Line of Charge with Variable Density
A rod extends along the x-axis from $$x = 0$$ to $$x = 0.8 \; m$$. Its linear charge density is give
Potential on the Axis of a Charged Disk
A thin circular disk of radius $$R = 0.15 \; m$$ has a uniform surface charge density of $$\sigma =
Testing the Relationship Between Electric Force and Distance in a Vacuum Chamber
Design an experiment to measure the force between two isolated charged objects in a vacuum chamber t
Uniform Electric Field in a Finite Charged Plate Experiment
An experiment is designed to verify the existence of a uniform electric field produced by a large, f
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 Electric Fields: Integral Calculation
Electric fields perform work on charges moving through them. Determine the work done in moving a cha
AC Response and Displacement Current in a Capacitor
A capacitor with capacitance $$C$$ is connected to an AC voltage source described by $$V(t) = V_0 \c
Analysis of Capacitors in Series and Parallel
A circuit contains three capacitors arranged such that capacitors $$C_1$$ and $$C_2$$ are connected
Analyzing Dielectric Constant Influence on Capacitance
When a dielectric is inserted into a capacitor, its capacitance increases. Consider the following ta
Analyzing Gradual Dielectric Insertion in a Capacitor
Gradually inserting a dielectric material into a capacitor can continuously change its capacitance.
Calculus Analysis of Electric Field and Potential in a Non-Uniform Capacitor
A parallel plate capacitor contains a non-uniform dielectric where the permittivity varies with dist
Capacitance of Cylindrical Conductors
Two long, coaxial cylinders act as a capacitor. The inner cylinder has radius $$a$$ and the outer cy
Capacitor Discharge Curve and Time Constant Computation
A capacitor in an RC circuit discharges over time, and its voltage follows the equation $$V(t)=V_0 e
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 a Complex Conductor
A complex-shaped conductor is studied to understand how its geometry affects surface charge density.
Combined Capacitance in Series and Parallel
Capacitors can be combined in series or parallel to achieve desired overall capacitance values. Anal
Composite Material Shielding Analysis
A Faraday cage is constructed using multiple layers of different conductive materials. Consider a ca
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 \(V(t) = V_0 * \sin(2 * \pi * f * t)\),
Dielectric Effects on Capacitance
A capacitor is tested under two conditions: with and without a dielectric material inserted between
Dynamic Parallel Plate Capacitor
A parallel plate capacitor is charged to a constant charge $$Q$$ but has a plate separation that inc
Effect of Dielectrics on Capacitance: A 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 Distribution on a Conductor
Consider an isolated conductor with a non‐uniform surface curvature. The local charge density, and h
Electric Field Mapping in a Multi-Conductor System
Consider a system consisting of two large, parallel conducting plates separated by a distance $$d$$
Electric Shielding and Faraday Cages
A sensitive electronic device is protected by being placed inside a Faraday cage made of a conductiv
Electric Shielding Efficiency in Faraday Cages
A researcher claims that a Faraday cage constructed with aluminum panels significantly reduces exter
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 Extraction from Capacitor Discharge in a Flash Circuit
A camera flash circuit utilizes a capacitor that rapidly discharges to produce a flash. Consider a c
Energy Storage in a Parallel Plate Capacitor
A parallel plate capacitor is used to store energy, and you are tasked with experimentally verifying
Energy Stored in a Capacitor Experiment
An experiment was conducted to measure the energy stored in a capacitor at different applied voltage
Experimental Analysis of Dielectric Breakdown
A researcher investigates the dielectric strength of several insulating materials. The experiment in
FRQ 2: Electric Shielding in a Sensor Enclosure
Sensitive biomedical sensors are enclosed in a metal box to protect them from external electromagnet
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 5: Impact of Dielectric Insertion on Capacitor Behavior
A laboratory experiment is performed in which the capacitance of a parallel plate capacitor is measu
FRQ 8: Dielectric Breakdown Analysis under Variable Frequencies
A dielectric material is subjected to an applied voltage at various frequencies. Experimental data s
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 11: Integration of Electric Field Lines on a Charged Plane
A laboratory experiment aimed to compute the electric flux through a large, flat charged plate by in
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 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 18: Non-linear Capacitance in Varactor Diodes
In a semiconductor laboratory, researchers study varactor diodes where the capacitance is non-linear
FRQ 20: Polarization Dynamics in Dielectrics under Strong Electric Fields
In a laboratory experiment, the polarization response of a polar dielectric is investigated by subje
Investigation of Dielectric Breakdown Voltage
A study was conducted to investigate the breakdown voltage of dielectric materials. The breakdown vo
Modeling Electric Field Interactions Between Two Conductors
When two conductors are placed in close proximity, their electric fields interact. Design an experim
Modeling Surface Charge Density and Curvature
For a conductor with non-uniform curvature, the local surface charge density $$\sigma(x)$$ is expect
Optimizing Conductive Coatings for Electric Shielding
Different conductive coatings can affect the effectiveness of electric shielding. Design an experime
Oscillatory Behavior in LC Circuits
An LC circuit can exhibit oscillatory behavior, and you are to design an experiment to measure the o
RC Filter Circuit Analysis
An RC circuit is used as a low-pass filter. Answer the following: (a) Derive the cutoff frequency $
Surface Charge Redistribution on Irregularly Shaped Conductors
An irregularly shaped conductor has varying curvature along its surface, leading to a non-uniform su
Temperature Effects on Dielectric Performance
A capacitor uses a dielectric material whose dielectric strength decreases linearly with temperature
Temperature Effects on Dielectric Strength
The dielectric constant of a material is temperature-dependent and is given by the relation $$k(T)=
Time-Varying Voltage Capacitor System
A capacitor of capacitance $$C$$ (with a dielectric) is connected to a voltage source that varies wi
Transient Analysis of Capacitor Charging in RC Circuits
Transient analysis of capacitor charging provides insight into the dynamic behavior of RC circuits.
Analysis of a Series Circuit with Variable Resistors
In a series circuit with two resistors, one of which is temperature-dependent, analyze the voltage d
Analysis of AC Circuit Frequency Effects
In an AC circuit, the voltage is described by $$V(t) = V_0 \sin(2\pi f t)$$ with $$V_0 = 10\,V$$ and
Analysis of Power Supply Stability
Examine a power supply circuit where the output voltage is affected by varying load conditions. Use
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
Application of Kirchhoff’s Current Law at a Complex Node
At a junction with multiple branches, apply Kirchhoff’s Current Law (KCL) and explore the implicatio
Calculating Power in a DC Circuit
A resistor of $$10\,\Omega$$ is connected to a battery supplying 18 V. Analyze the electric power co
Capacitor Charging Diagram Analysis
A graph is provided that represents the capacitor charging process in an RC circuit. Analyze the dia
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 Series and Parallel Combination
Three capacitors with capacitances $$C_1 = 4\,\mu F$$, $$C_2 = 6\,\mu F$$, and $$C_3 = 8\,\mu F$$ ar
Capacitors in Series and Parallel Combination in Sensor Circuits
In a sensor circuit, four capacitors are arranged such that three capacitors (C1, C2, C3) are connec
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
Circuit Design with Series and Parallel Components
This question requires you to analyze a circuit that contains a combination of series and parallel r
Determining Material Effects on Resistance
In an experiment comparing wires of different materials but identical dimensions, measurements of re
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 $$R_0=50\;
Electrolytic Capacitor Behavior Experiment with Misinterpretation of Dielectric Absorption
An experiment is carried out to measure the charging and discharging curves of an electrolytic capac
Energy Analysis of a Constant Power Load in a DC Circuit
A DC circuit supplies a constant power output to a load over a period of time. Analyze the energy de
Energy Storage in Capacitors and Inductors
Using calculus, derive the expressions for the energy stored in (a) a capacitor with capacitance C c
Evaluating Measurement Errors in Circuit Instruments
Measurement errors in electrical instruments can propagate through calculations. Evaluate the error
Evaluating Oscilloscope Measurement Accuracy in AC Circuits
During an experiment, voltage waveforms captured by an oscilloscope showed slight distortions compar
FRQ 3: Parallel Circuit Analysis
A circuit has three resistors connected in parallel to a $$12\,V$$ battery. The resistors have value
FRQ 8: Kirchhoff's Current Law at a Node
At a junction in a circuit, three branches converge. Two of the branches have measured currents of $
FRQ 10: EMF and Internal Resistance Determination via Calculus
A battery is tested under various load conditions. The following experimental data is recorded: | L
FRQ 15: RC Oscillator Analysis
An RC oscillator circuit is designed to generate a periodic waveform. The circuit uses a resistor (R
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
Ideal Versus Non-Ideal Circuit Component Analysis
Theoretical models using ideal circuit components often predict behavior that deviates from experime
Impedance in a Series RLC Circuit
This question involves analyzing the impedance of a series RLC circuit connected to an AC source. Yo
Impedance Variation with Frequency in a Series RLC Circuit
A researcher investigates the impedance of a series circuit containing a resistor, an inductor, and
Inductor Energy Dissipation in a DC Circuit
Consider a circuit where an inductor (L = 0.5 H) is connected in series with a resistor (R = 20 \(\O
Internal Resistance Effects on Battery Performance
An experiment was performed to study the effects of load current and ambient temperature on a batter
Kirchhoff's Voltage Law in a Complex Circuit
Consider a circuit where three resistors (R1, R2, and R3) are connected in series with a battery of
Network Analysis Using Kirchhoff's Laws
A laboratory experiment involves analyzing an electrical network that consists of a voltage source o
Parallel Circuit Analysis Using Kirchhoff's Current Law
A DC circuit consists of three resistors connected in parallel to a 24 V battery. The resistor value
Parallel Circuit Behavior Experiment
In a parallel circuit, resistor branches were connected across a constant voltage source. The table
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 and Energy in a Resistive Circuit
A resistive circuit is powered by a constant current source. Examine the energy transfer in the resi
Power, Energy, and Efficiency in Electric Circuits
Analyze the energy consumption in a resistor when the current varies with time. Consider a resistor
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 Design
An engineer is designing an RC low-pass filter to attenuate frequencies above 1 kHz. The filter is c
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 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 Analysis with Time-Varying Source
Analyze a resistive series circuit with three resistors and a battery whose voltage is modulated by
Series Circuit Voltage Distribution Error in Measurement
In an experiment on a series circuit, a student measures the voltage drops across several resistors
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 Analysis of an RL Circuit
A researcher studies the transient response of an RL circuit consisting of a resistor $$R=100\,\Omeg
Transient Analysis of an RLC Circuit with Error in Damping Factor Estimation
A student constructs an RLC circuit to study its transient response to a step input voltage. The pro
Transient Behavior in a Combined RC and RL Circuit
A researcher studies a circuit that combines elements of both RC and RL circuits. In this circuit, t
Variable Resistor and Thermistor Behavior Analysis
A variable resistor in a circuit is adjusted to change its voltage drop linearly with rotation. Addi
Voltage Divider with Variable Resistor
A voltage divider circuit is built using a fixed resistor and a variable resistor. Investigate how t
Advanced Analysis of Magnetic Interaction in Particle Accelerators
In particle accelerators, charged particles are deflected by magnetic dipole fields. (a) Derive th
Ampère’s Law in a Toroid
A researcher designs a toroid and wishes to determine the magnetic field inside its core. Given the
Analyzing a Magnetic Resonance Experiment
In a magnetic resonance experiment, a sample is placed in a uniform static magnetic field of 1.5 T a
Application of Biot–Savart Law for a Finite Wire Segment
A finite straight wire segment carries a current I. (a) Use the Biot–Savart law to derive an integ
Calculus Application: Variable Current and Magnetic Field
A wire has a current that varies along its length according to $$I(x) = I_0*(1 + x)$$, where x is in
Charged Particle in a Spatially Varying Magnetic Field
A charged particle with mass $$m$$ and charge $$q$$ moves in a magnetic field that varies spatially
Combined Effect of Electric and Magnetic Fields on a Charged Particle
An experiment claims that when a charged particle moves in a region containing both electric and mag
Combined Electric and Magnetic Field Effects on a Charged Particle (Velocity Selector)
A charged particle is introduced into a region where it experiences both perpendicular electric and
Comparison of Magnetic Fields Inside and Outside a Solenoid
Measurements were taken of the magnetic field in and around a long solenoid. The data in the table b
Critical Analysis of Ampère's Law in a Non-Uniform Magnetic Field
An experiment uses a loop to measure the magnetic field in a region where the field is non-uniform.
Current Variation and Magnetic Field Strength
In an experiment, the magnetic field is measured at a fixed distance from a straight conductor while
Dependence of Magnetic Field Strength on Distance
A long straight wire carries a current of 10 A. (a) Derive an expression for the magnetic field as a
Design Considerations for an Electric Motor Component
Electric motors use current-carrying loops in magnetic fields to generate torque. Consider the desig
Determination of Torsional Stiffness of a Wire Using Magnetic Torque
A student investigates the torsional stiffness of a wire by attaching a rectangular current-carrying
Determining Torsional Stiffness from Experimental Data
A wire is subjected to various applied torques causing it to twist by different angles θ. The torsio
Determining Torsional Stiffness of a Twisted Wire
A wire is twisted by applying a torque, leading to an angular displacement. The relation is given by
Effect of Number of Turns on a Solenoid's Magnetic Field
In a study of a solenoid's magnetic field, researchers varied the number of turns in the coil while
Evaluating Forces in a Crossed Electric and Magnetic Field
A charged particle with mass $$m = 9.11*10^{-31}\,kg$$ and charge $$q = -1.6*10^{-19}\,C$$ is initia
Experimental Analysis: Magnetic Field Strength vs. Distance Using the Right-Hand Rule
A study reports that the magnetic field strength around a current-carrying wire decreases inversely
Experimental Determination of Torsional Stiffness
A researcher investigates the torsional stiffness of a thin metallic wire by measuring the torque re
Experimental Verification of the Right-Hand Rule for Magnetic Fields
An experimental setup uses a curved current-carrying wire and sensitive magnetic field sensors place
Force Between Two Parallel Current-Carrying Wires
Two long, parallel wires separated by distance d carry currents I₁ = 4 A and I₂ = 4 A in the same di
Force Interaction Between Parallel Current-Carrying Wires
Design an experiment to measure the force of interaction between two parallel current-carrying wires
Force on a Curved Current-Carrying Arc
A curved wire in the shape of an arc with radius R and central angle $$\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
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 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
Lorentz Force in a Particle Accelerator
A high-energy physics experiment report claims that the Lorentz force \(F = q*v*B\) acting on charge
Lorentz Force on a Moving Charged Particle
A charged particle with charge $$q$$ moves with velocity $$v$$ perpendicular to a uniform magnetic f
Magnetic Dipole Moment from Torque Measurements
A current loop experiences a maximum torque when placed in a uniform magnetic field. (a) Derive an
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 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 Solenoid
Examine the magnetic field produced inside a solenoid. Derive its theoretical expression and compare
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 Measurement around a Straight Conductor
An experimental setup is constructed to measure the magnetic field around a long straight conductor
Magnetic Field of a Circular Conductor Loop Investigation
Design an experiment to study the magnetic field both inside and outside a circular loop of current-
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 Strength Inside a Solenoid with Varying Coil Turns
A research report states that the magnetic field inside a solenoid increases linearly with the numbe
Magnetic Field within a Solenoid
A solenoid 0.50 m in length contains 1000 turns and carries a current of 2.0 A. Using the formula $$
Non-Uniform Current Density and Magnetic Field Distribution
A recent theoretical investigation claims that for conductors with non-uniform current density, the
Non-Uniform Magnetic Field Study in a Solenoid
Design an experiment to measure the variation of the magnetic field along the length of a solenoid w
Optimization of MRI Magnetic Field Strength
An MRI machine design requires a highly uniform and strong magnetic field, generated by a solenoid.
Spatial Mapping of Magnetic Field Vectors in a Wire Array
An array of parallel current-carrying wires is arranged, and a 3D Hall probe is used to measure the
Superimposed Magnetic Fields from Concentric Loops
Two concentric circular loops with radii $$R_1$$ and $$R_2$$ carry currents $$I_1$$ and $$I_2$$ resp
Superposition of Magnetic Fields from Multiple Coils
An array of N identical circular coils (each with radius R and carrying current I) is arranged along
Torque on a Current Loop
A rectangular loop carrying a current is placed in a uniform magnetic field. (a) Derive an express
Torque on a Twisted Current-Carrying Wire
Design an experiment to measure the torque produced on a twisted current-carrying wire placed in an
Velocity Selection in a Particle Detector
A particle detector is designed using crossed uniform electric $$E$$ and magnetic $$B$$ fields that
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
Analysis of Energy in an Inductor and LR Circuit
An LR circuit, consisting of an inductor with inductance L and a resistor R, is connected to a const
Analysis of Lenz's Law via a Coil and Falling Magnet Experiment
In an experiment, a magnet is dropped through a copper tube and coils wrapped around the tube record
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 Displacement Current in a Charging Capacitor
In a parallel-plate capacitor being charged by a current $$I$$, the electric field between the plate
Application of Gauss's Law to a Charged Sphere
A solid sphere with total charge $$Q$$ is uniformly charged throughout its volume.
Calculating Coiled Inductance via Magnetic Flux
A solenoid with $$N$$ turns has a cross-sectional area $$A$$ and is placed in a uniform magnetic fie
Deriving Generated EMF in a Rotating Generator
In an electric generator, a coil rotates with constant angular speed $$\omega$$ inside a uniform mag
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
Designing an Induction Heating System
An induction heating system is designed to heat a metallic workpiece using a coil that induces eddy
Determination of Inductance via Flux Linkage
An experiment is conducted to determine the inductance of a coil by measuring the magnetic flux as a
Determining Inductance from a Current Ramp
A single inductor with unknown inductance L is subjected to a linearly increasing current described
Eddy Current Braking Analysis
A rotating metallic disk is subjected to a magnetic field, and eddy currents are induced which produ
Electromagnetic Braking System: Analysis and Design
Electromagnetic braking utilizes Lenz's law where induced currents produce forces that oppose the mo
Electromagnetic Oscillator Simulation
A circuit is designed incorporating an LC oscillator with a resistor to simulate damping, resulting
Energy Storage in an Inductor
An inductor with inductance $$L=0.50\;H$$ carries a time-dependent current given by $$I(t)=5t\;(A)$$
Estimating Inductance from LR Circuit Data
An experimental LR circuit is used to determine the inductance $$L$$ of an unknown coil. The circuit
Experimental Evaluation of Induced EMF
An experiment measured the induced EMF in a rotating coil at various angles. The following data is p
Experimental Validation of Faraday's Law
The following table provides experimental measurements of magnetic flux through a coil over time.
Graphical Analysis of Changing Magnetic Flux
A graph of magnetic flux $$\Phi(t)$$ versus time is provided. Use the graph to analyze the induced E
Induction Heating and Eddy Current Analysis
An induction heater uses electromagnetic induction to heat a metal object. The magnetic flux through
Induction Heating and Eddy Currents
A metal plate is placed above an induction coil that produces a spatially uniform alternating magnet
Induction Heating and Eddy Currents
In an induction heating device, a time-varying magnetic field is produced by an alternating current
Induction Motor Back EMF Analysis
This problem focuses on the analysis of back EMF in an induction motor, including its derivation and
Inductor Energy Storage and Discharge
An inductor with inductance $$L$$ carries a steady current $$I$$, thereby storing magnetic energy in
Investigating Induced EMF in a Rotating Loop
A conducting loop of area $$A$$ rotates in a uniform magnetic field $$B$$ with constant angular velo
Magnetic Field Calculation Inside a Solenoid
This problem requires the use of Ampere's Law to determine the magnetic field inside a long solenoid
Magnetic Field Distribution and Gauss's Law
A uniformly charged sphere produces an electric field that varies with the distance from the center.
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 Levitation Analysis
Evaluate a magnetic levitation system where an object of mass $$m$$ is levitated by electromagnetic
Magnetic Levitation via Electromagnetic Induction
In a magnetic levitation system, coils are used to create dynamically varying magnetic fields that i
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
Modeling Anomalous EMF Signals in an Induction Experiment
Experimental data from an induction experiment shows that the induced EMF does not follow an ideal s
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 Determination in an LC Circuit
An LC circuit is constructed using a capacitor of capacitance $$C = 100\,\mu F$$ and an unknown indu
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
Resonant Frequency Variation in an LC Circuit
An LC circuit consists of an inductor with inductance $$L$$ and a variable capacitor with capacitanc
Sensitivity of Resonant Frequency to Component Changes in an LC Circuit
The resonant frequency of an LC circuit is given by $$f = \frac{1}{2\pi\sqrt{L*C}}$$.
Sinusoidal EMF from an Alternating Current Generator
A researcher investigates an AC generator where a coil rotates in a magnetic field, producing a sinu
Time Constant in an LR Circuit
An experiment is performed to determine the time constant of an LR circuit by measuring the rise of
Transformer Efficiency Investigation
This problem examines the relationships in an ideal transformer and explores how various factors aff
Transient Analysis in an LR Circuit
Consider an LR series circuit with resistance $$R$$ and inductance $$L$$. At time $$t = 0$$, a switc
Transient Behavior Analysis in an LR Circuit
A researcher examines the transient current behavior in an LR circuit immediately after the switch i
Transient Response in an RLC Circuit (Series)
This problem examines the transient oscillatory response of a series RLC circuit undergoing underdam
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
Verification of Gauss's Law for Electric Fields
A sphere of radius $$R$$ has a charge density given by $$\rho(r) = \rho_0 \left(\frac{r}{R}\right)^2
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.