AP Physics C: Electricity and Magnetism FRQ Room

Analysis of Electric Field Lines

Examine the following diagram representing electric field lines produced by a positive and a negativ

Applying Gauss' Law for a Spherical Conductor

In a lab experiment, the electric flux through spherical surfaces of various radii is measured aroun

Calibrated Probe Measurements of Electric Field Strength in a 2D Plane

A set of calibrated probes measures the electric field at various (x, y) positions within a planar r

Capacitor Charging Experiment

A capacitor with capacitance $$C = 10 \; \mu F$$ is charged through a resistor with resistance $$R =

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 on a Conducting Sphere

This problem asks you to discuss the equilibrium charge distribution on a conducting sphere and then

Charge Interaction in Mixed Media

A computer simulation investigates how two point charges interact when placed in media with differen

Computation of Electric Flux Through a Curved Surface

A curved surface is placed in a uniform electric field. The cumulative electric flux through the sur

Conductors in Electrostatic Equilibrium

A hollow metallic (conducting) sphere is uniformly charged with a total charge $$Q$$ and contains an

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 Investigation

In a laboratory experiment, two point charges are placed on an insulating table. One charge has a va

Data Analysis of Electric Force Measurements

In a laboratory experiment, the force between charged spheres was measured at various distances. Usi

Designing an Experiment to Measure the Electric Field due to a Cylindrical Charge Distribution

Design an experiment to measure the electric field around a long, uniformly charged cylinder using a

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 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 from a Point Charge

A single point charge creates an electric field in the space around it. Analyze the electric field p

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 in a Non-uniform Charge Distribution on a Plate

An experiment investigates the electric field produced by a non-uniformly charged insulating plate.

Electric Field of a Charged Ring: A Calculus Approach

A ring of radius $$R$$ carries a uniform charge distribution with total charge $$Q$$. Determine the

Electric Field of a Non-Uniformly Charged Cylinder

Consider a long cylinder of length L with a linear charge density that varies along its length as $$

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 through a Non-spherical Surface

An electric field originating from a point charge is present and you are to evaluate the electric fl

Electric Potential and Work Done by Electric Field

A test charge of 2 C is moved along the x-axis in a region where the electric potential is given by

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 Energy of a Uniformly Charged Rod

Derive an expression for the electric potential energy stored in a uniformly charged rod and discuss

Electric Potential from a 3D Charge Distribution in a Cube

A researcher is studying the electric potential at the origin due to a three-dimensional charge dist

Electric Potential from a Uniformly Charged Rod

This problem requires you to derive the electric potential at a point on the perpendicular bisector

Electrostatic Equilibrium in Conductors

A researcher investigates the behavior of electric charges in a conductor connected to a voltage sou

Electrostatic Induction and the Faraday Cage

A researcher is exploring electrostatic induction and the effectiveness of a Faraday cage in shieldi

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

Evaluating the Charge on a Sphere using Measured Electric Field Data

This problem starts with experimental data of the radial electric field from a charged sphere and as

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

Field and Potential from an Infinite Sheet of Charge

An infinite sheet has a uniform surface charge density of $$\sigma = 4.0 \times 10^{-6} \; C/m^2$$.

Field Inside and Outside a Charged Sphere

A non-conducting sphere of radius $$R = 0.20 \; m$$ carries a uniformly distributed charge of $$Q =

FRQ 1: Evaluation of Coulomb's Law Experiment

A physicist conducted an experiment to measure the electrostatic force between two small charged sph

FRQ 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 14: Analysis of Electrostatic Force Variation with Distance

A researcher claims that the measured electrostatic force between two point charges precisely follow

FRQ 17: Experimental Analysis of the Relationship $$E = -\nabla V$$

A media report claims that experimental measurements of the spatial gradient of electric potential v

FRQ 18: Critical Analysis of Coulomb's Law in a High Vacuum Environment

A scientific paper asserts that in high vacuum conditions, experimental measurements of the force be

Gauss' Law in a Cylindrical Charge Distribution

An infinitely long cylinder of radius R carries a uniform volume charge density ρ. Use Gauss’s law t

Gauss' Law in Practice: Flux Calculation for a Charged Cylinder

Develop an experimental proposal to measure the electric flux through a cylindrical surface surround

Integration of Electric Field over a Path in a Non-Uniform Field

In a physics laboratory, an experiment is carried out to measure the potential difference along a pa

Investigating Electric Fields in Conductors vs. Insulators

Design an experiment to compare the electric field distribution around a metallic (conductor) sphere

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

Mapping the Electric Field of a Charged Sphere

Design an experiment to map the electric field around a uniformly charged insulating sphere using a

Measuring Electric Field Lines using Near-field Probes

In this experiment, a set of movable near-field probes is used to measure the spatial variation of t

Multi-Charge Interaction Analysis

Three point charges are located at the vertices of an equilateral triangle with side length $$0.10 \

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)

Optimization of Non-uniform Charge Distribution

A researcher aims to optimize the electric field at a point P on the y-axis (distance $$d$$ from the

Point Charge Interaction Experiment

Two point charges are fixed in space, and an experiment is carried out to measure the force experien

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 =

Superposition of Electric Potentials

This problem involves calculating the net electric potential at a point due to two point charges usi

Surface Charge Distribution and Field Just Outside a Conductor

A metal sphere of radius $$0.10 \; m$$ is uniformly charged with a total charge of $$Q = 1.0 \times

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

Transient Behavior in an RC Circuit

A researcher studies the transient discharge of a capacitor in an RC circuit.

Uniformly Charged Sphere: Electric Field and Potential

A sphere of radius $$R$$ carries a uniform charge distribution with a total charge $$Q$$. Analyze th

Work and Energy in a Uniform Electric Field

A particle with charge q = 1 C is accelerated from rest by a uniform electric field of magnitude E =

Work Done by a Uniform Electric Field

This problem examines the work done on a charged particle as it moves in a uniform electric field an

Work Done by Electric Fields: Integral Calculation

Electric fields perform work on charges moving through them. Determine the work done in moving a cha

Work Done in a Non-Uniform Electric Field

This question requires you to compute the work done on a charge moving through a spatially varying (

Analysis of Capacitor Charging Curve

A capacitor charging experiment was performed where the voltage across the capacitor was recorded ov

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

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 Charging with a Time-Varying Voltage Source

Consider a circuit where a capacitor of capacitance $$C$$ is connected through a resistor $$R$$ to a

Capacitor in a Time-Varying External Electric Field

A parallel plate capacitor is placed in an external time-varying electric field given by $$E_{ext}(t

Capacitors in AC Circuits with Dielectrics

A researcher analyzes a capacitive circuit with a ceramic capacitor in an AC circuit powered by a si

Combined Capacitance in Series and Parallel

Capacitors can be combined in series or parallel to achieve desired overall capacitance values. Anal

Comparative Analysis of Capacitor Types in High-Frequency Applications

Different types of capacitors (ceramic, electrolytic, and film) exhibit varying performance characte

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

Design and Analysis of a Capacitor Bank for Energy Storage

For a high-energy application, a capacitor bank must be designed to store 1000 joules of energy at 1

Design and Analysis of a Faraday Cage

A researcher is designing a Faraday cage to shield sensitive electronic equipment from external elec

Designing a Faraday Cage for Sensitive Instrumentation

A sensitive piece of instrumentation must be shielded from external electromagnetic interference. Yo

Designing a Faraday Cage for Sensitive Instruments

A research team is tasked with designing a Faraday cage to protect sensitive electronic equipment fr

Dielectric Breakdown Analysis

Dielectric breakdown occurs when a dielectric material is exposed to an electric field that exceeds

Dielectric Effects on Capacitance

A capacitor is tested under two conditions: with and without a dielectric material inserted between

Dielectric Effects on Capacitor Performance

A parallel plate capacitor is initially filled with air. A dielectric slab of thickness $$d$$ and di

Effect of Dielectric Material on Capacitor Performance

A capacitor’s performance can be significantly altered by the introduction of a dielectric material

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 Conducting Surface

A conductor possesses regions with different curvatures including a flat area and a sharply curved t

Electric Field Distribution on a Conductor

Consider an isolated conductor with a non‐uniform surface curvature. The local charge density, and h

Energy Density Analysis in a Capacitor With a Non-Uniform Electric Field

A capacitor has an electric field that varies with position according to $$E(x) = \frac{V}{d + a \cd

Energy Dissipation in a Discharging Capacitor

A capacitor with initial voltage $$V_0$$ and capacitance $$C$$ discharges through a resistor $$R$$.

Energy Storage in a Parallel Plate Capacitor

A parallel plate capacitor is used to store energy, and you are tasked with experimentally verifying

FRQ 1: Electrostatic Equilibrium in Conducting Spheres

In this experiment, a uniformly charged metal sphere is allowed to reach electrostatic equilibrium.

FRQ 2: Electric Shielding in a Sensor Enclosure

Sensitive biomedical sensors are enclosed in a metal box to protect them from external electromagnet

FRQ 4: Dielectric Insertion in a Parallel-Plate Capacitor Experiment

In this experiment, a capacitor’s capacitance was measured as a dielectric slab was slowly inserted

FRQ 4: Distance Dependence of a Parallel Plate Capacitor

In this experiment, a parallel plate capacitor with fixed area and dielectric material is used. The

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 13: Mitigating Electromagnetic Interference in Portable Devices

A study is conducted to measure the effectiveness of different smartphone case materials in reducing

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 16: Optimizing Faraday Cage Design

An engineering team is testing Faraday cages made with different mesh sizes and metal thicknesses to

FRQ 17: Dynamic Capacitance Variation with Frequency in a Dielectric

In this experiment, a capacitor with an inserted dielectric is connected to an AC voltage source wit

FRQ 19: Modeling Capacitance of a Non-Standard Geometric Capacitor

A researcher built a capacitor with non-parallel, curved plates to investigate how plate curvature a

Geometry Effects on Electric Field Distribution

The local electric field strength on a conductor’s surface varies with its curvature. Design an expe

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.

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

Non-Ideal Capacitor Discharge in a Resistive-Capacitive Network

A non-ideal capacitor discharges through a resistor and also loses charge via a constant leakage cur

Parallel Plate Capacitor with Non-uniform Plate Separation

A parallel plate capacitor has one plate fixed while the other plate is slightly curved so that the

Partial Dielectric Insertion and Effective Capacitance

Consider a parallel plate capacitor with plate area \(A\) and plate separation \(d\). A dielectric s

Surface Charge Redistribution on Irregularly Shaped Conductors

An irregularly shaped conductor has varying curvature along its surface, leading to a non-uniform su

Transient Response in an RC Circuit with Variable Resistance

Consider an RC circuit in which the resistor’s value varies with time as $$R(t)=R_0\,(1+\alpha t)$$,

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

Variable Capacitors in Tuning Circuits

Variable capacitors are used in tuning circuits where their capacitance can be adjusted by changing

AC Analysis of a Series RLC Circuit

An RLC series circuit operates with an alternating current signal. Analyze its impedance and phase c

Analysis of a Non-Ideal Battery Circuit

A non-ideal battery with an electromotive force (EMF) of 12 V and an internal resistance of $$r = 1$

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

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 Power Factor in an AC Circuit

In an AC circuit, the voltage and current are given by $$V(t)=120*\sin(2*\pi*60*t)$$ and $$I(t)=10*\

Analyzing Conduction in AC vs DC Circuits

Data was collected from both AC and DC circuits measuring voltage and current across a resistor unde

Capacitors in Parallel: Charge Distribution

Two capacitors, $$C_{1}=4\,\mu F$$ and $$C_{2}=8\,\mu F$$, are connected in parallel to a $$10\,V$$

Circuit Design Challenge: Maximizing Power Transfer

A circuit is designed to maximize power transfer to a load resistor. Using the Thevenin equivalent c

Designing an RC Low-Pass Filter

A low-pass filter can be constructed using a resistor and capacitor. Determine the filter characteri

Digital Circuit Analysis: Logic Analyzer and Current Measurement

In a digital circuit, a logic analyzer is used to capture the state of digital signals, and current

Electromagnetic Induction Experiment with Misinterpreted Rate of Change

A student performs an experiment to measure the induced electromotive force (EMF) in a coil when a m

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 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 \(50\,V\).

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 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 $

Impedance Measurement in AC Circuits with Ignored Inconsistent Source Behavior

An experiment is conducted to measure the impedance of a complex AC circuit at various frequencies.

Investigating the Effect of Variable Resistance on Circuit Current

A variable resistor (potentiometer) is used in a DC circuit powered by a 12 V battery. Experimental

Kirchhoff's Current Law Node Analysis

A node in a circuit receives current from a 20 V source and splits into three branches with resistor

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

KVL and Energy Conservation in a Closed Loop

A student asserts that, in any closed circuit loop, the algebraic sum of the voltage drops is exactl

Measuring Power Dissipation in Resistive Circuits

This question examines the derivation of power relationships in resistive circuits and requires you

Misinterpretation of Impedance in High-Frequency Circuits

A researcher performs an experiment on a high-frequency AC circuit designed to emulate a transmissio

Multi-Loop Circuit Analysis using Kirchhoff's Laws

A circuit consists of two loops that share a common resistor. A student claims that by applying Kirc

Non-Linear Resistor Behavior in Thermistors

Thermistors exhibit a non-linear relationship between voltage and current due to their temperature d

Parallel Circuit Analysis and Power Distribution

An industrial circuit powered by a 48 V source supplies three branches connected in parallel. The br

Power Dissipation in a Resistive Circuit with Internal Battery Resistance

A circuit contains a battery with an EMF of 9 V and an internal resistance of 0.5 Ω connected in ser

Power, Energy, and Efficiency in Electric Circuits

Analyze the energy consumption in a resistor when the current varies with time. Consider a resistor

RC Charging Circuit Analysis

In an RC circuit, a capacitor with capacitance $$C=10\,\mu F$$ is charged through a resistor with $$

RC Discharging Circuit Analysis

A capacitor initially charged to $$20\,V$$ discharges through a resistor with $$R=5000\,\Omega$$ and

RC Low-Pass Filter Frequency Response Analysis

A research group hypothesizes that an RC low-pass filter attenuates high-frequency signals such that

Series Circuit Analysis and Power Calculation

In a household series circuit, a battery supplies a total voltage of $$V = 24$$ V to three resistors

Series Circuit Analysis with Calculus Application

A researcher is investigating a series circuit in which three resistors (with initial values $$R_{1}

Series Circuit Analysis with Time-Varying Source

Analyze a resistive series circuit with three resistors and a battery whose voltage is modulated by

Simultaneous Application of Ohm's and Kirchhoff's Laws

Consider a circuit consisting of two loops. The first loop has a battery of 15 V, a resistor $$R_1 =

Studying Frequency Effects on RC Oscillators

An RC oscillator was tested, and its oscillation frequency was recorded for various resistor and cap

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 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 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 in RC Charging Circuit

In an RC circuit with resistor R = 10 Ω and capacitor C = 100 μF, the capacitor is initially uncharg

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

Variable Resistor and Thermistor Behavior Analysis

A variable resistor in a circuit is adjusted to change its voltage drop linearly with rotation. Addi

Application of Ampère’s Law in a Toroid

A toroid with a rectangular cross-section has 500 turns and a mean radius of 0.10 m and carries a cu

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

Bar Magnet Field Distribution Analysis

Design an experiment to map the spatial distribution of the magnetic field around a bar magnet. Incl

Calculating Magnetic Field from a Wire with Non-uniform Current Density

A long, thin wire has a current density that varies along its length according to $$J(x) = J_0(1 + 0

Calculus of Magnetic Field Lines

A researcher wishes to derive a differential equation that describes the magnetic field lines around

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 Electric and Magnetic Forces on a Moving Charge

A particle with charge $$q = 2*10^{-6}\,C$$ moves with a velocity $$\vec{v} = (3\hat{i} + 4\hat{j})\

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

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 Distribution in a Solenoid with Variable Turn Density

Consider a solenoid of length $$L = 1.0\,m$$ where the density of turns per unit length varies accor

Current Variation and Magnetic Field Strength

In an experiment, the magnetic field is measured at a fixed distance from a straight conductor while

Design Considerations for an Electric Motor Component

Electric motors use current-carrying loops in magnetic fields to generate torque. Consider the desig

Designing and Analyzing a Helmholtz Coil Arrangement

In a Helmholtz coil configuration, two identical circular coils of radius $$R$$ are separated by a d

Determining Torsional Stiffness from Angular Deflection Data

A metal wire is twisted by applying varying torques. The resulting angular deflection (in radians) w

Effect of Magnetic Field Direction Change on a Moving Charged Particle

Design an experiment to study the effect of changing the direction of a magnetic field on the deflec

Effect of Wire Geometry on Magnetic Field Distribution

Consider two wires carrying the same current I: one is a straight wire and the other is bent into a

Evaluating Magnetic Field Distribution in a Halved Solenoid

A long solenoid is physically divided into two equal halves. (a) Using integration, derive express

Evaluation of Magnetic Field Produced by Parallel Current-Carrying Wires

In a lab experiment, two parallel wires carrying identical currents are set up with variable spacing

Experimental Analysis of Increased Coil Turns on Magnetic Field Strength

An engineering study claims that increasing the number of turns in a coil leads to a linear increase

Experimental Validation of the Right-Hand Rule

An experiment is designed to validate the right-hand rule by measuring the direction of the magnetic

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 Parallel Current-Carrying Wires

Two long, parallel wires separated by a distance \(d\) carry currents \(I_1\) and \(I_2\). They exer

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 on a Current-Carrying Wire in a Magnetic Field

A wire of length $$L$$ carrying a current $$I$$ is placed in a uniform magnetic field $$B$$ making a

Force on a Current-Carrying Wire in a Magnetic Field

A wire of length L = 0.5 m carrying a current of I = 6 A is placed in a uniform magnetic field of B

Force on a Current-Carrying Wire in a Non-Uniform Magnetic Field

Consider a straight wire of length $$L$$ carrying a constant current $$I$$ along the x-axis. The wir

Force on a Current-Carrying Wire in an External Magnetic Field

An experiment measured the force on a current-carrying wire placed in an external magnetic field at

Force on a Current-Carrying Wire in an External Magnetic Field

A physics demonstration asserts that the force on a current-carrying wire in an external magnetic fi

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

Magnetic Dipole-Dipole Interaction Energy

Consider two magnetic dipoles, each with magnetic moment $$m$$, separated by a distance $$d$$. Using

Magnetic Field Distribution around a Bar Magnet

A bar magnet produces a magnetic field that is strongest near its poles. Explore the variation in fi

Magnetic Field in a Circular Loop - Claim Evaluation

A recent research paper claims that the magnetic field produced inside a circular current-carrying l

Magnetic Field in a Toroid

A toroid is a solenoid bent into a circular shape. Consider a toroid with inner radius $$a$$, outer

Magnetic Field Inside a Solenoid

A solenoid is a coil of wire with a large number of turns. Consider a solenoid of length $$L$$, with

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 Mapping of a Bar Magnet

A bar magnet is used to measure the magnetic field strength along its axial line. The following tabl

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 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 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 an infinitely long straight wire carrying a constant current. Use the standard formula deri

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 Force in a Particle Detector

In a particle detector, a charged particle with mass $$m$$, charge $$q$$, and velocity $$v$$ moves p

Magnetic Force on a Moving Charged Particle

In a controlled laboratory experiment, a charged particle with charge $$q = 2\times10^{-6} \; C$$ an

Measurement of Magnetic Field Using a Hall Probe

A researcher employs a Hall probe to measure the magnetic field around a current-carrying conductor.

Measuring the Lorentz Force on a Moving Charged Particle

A charged particle with charge $$q = 1.6 \times 10^{-19}\,C$$ is accelerated to a velocity of $$2 \t

Modeling the Interaction of Multiple Magnetic Sources

A region of space contains two distinct magnetic field sources: (1) a long straight wire along the y

Net Magnetic Field in a Helmholtz Coil Setup

A Helmholtz coil consists of two identical circular coils of radius 0.12 m, separated by 0.12 m alon

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 Current-Carrying Loop

A rectangular current loop with dimensions 0.10 m by 0.15 m carries a current of 3 A. It is placed i

Torque on a Current-Carrying Loop in a Magnetic Field

A rectangular current-carrying loop is placed in a uniform magnetic field. The torque on the loop is

Verification of the Biot–Savart Law

Design an experiment to verify the Biot–Savart Law by mapping the magnetic field produced by a small

AC Generator and Induced Current Analysis

An AC generator produces a time-varying EMF described by $$\epsilon(t)= 50*\cos(100*t)$$ (volts). Co

Analyzing Back EMF in an LR Circuit

Consider an LR circuit where, after a steady state current has been established, the applied voltage

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

Application of Gauss's Law to a Charged Sphere

A solid sphere with total charge $$Q$$ is uniformly charged throughout its volume.

Derivation of the Electromagnetic Wave Equation

Starting from Maxwell's equations in free space, derive the wave equations for both the electric fie

Designing an Electromagnetic Braking System

Electromagnetic braking systems use induced currents to generate a retarding force in moving vehicle

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 LR Circuit Transient Analysis

This problem explores the transient response of an LR circuit when a constant voltage is applied.

Determining Inductance from a Current Ramp

A single inductor with unknown inductance L is subjected to a linearly increasing current described

Displacement Current in a Charging Capacitor

A researcher investigates the role of displacement current in a capacitor circuit being charged by a

Electromagnetic Generator Analysis

A simple AC generator consists of a rectangular loop with area $$A=0.10\;m^2$$ rotating in a uniform

Electromagnetic Oscillator Simulation

A circuit is designed incorporating an LC oscillator with a resistor to simulate damping, resulting

Energy Transfer in LC Oscillations

An LC circuit oscillates with an initial charge $$Q_0$$ on the capacitor. The circuit consists of an

Estimating Inductance from LR Circuit Data

An experimental LR circuit is used to determine the inductance $$L$$ of an unknown coil. The circuit

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 $

Experimental Evaluation of Induced EMF

An experiment measured the induced EMF in a rotating coil at various angles. The following data is p

Flux Variation in a Rotating Coil

A circular coil with an area of 0.03 m² rotates in a uniform magnetic field of 0.8 T with a constant

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

Induced EMF in a Rotating Loop

A rectangular loop of wire with area A rotates with a constant angular speed $$\omega$$ in a uniform

Inductance in an LR Circuit

An LR circuit is constructed with an inductor of unknown inductance $$L$$ and a resistor of resistan

Inductive Heating and Eddy Currents

This problem explores the concept of inductive heating and the generation of eddy currents due to a

Interpreting a Visual Diagram of Magnetic Dipole Fields

A diagram of a bar magnet with magnetic field lines is provided. Analyze the diagram based on the fo

Investigation of Damped Oscillations in an LC Circuit

An experiment is conducted to study damped oscillations in an LC circuit. A capacitor is charged and

Investigation of Magnetic Flux Variation with Coil Orientation

An experiment is set up where a coil rotates at constant angular speed in a uniform magnetic field.

LC Circuit Damping Effects

An LC circuit is modified by adding a resistor, resulting in damped oscillations in the voltage acro

LC Circuit Resonance Analysis

An LC circuit oscillates due to the energy exchange between an inductor (with inductance $$L$$) and

Magnetic Field Mapping using Gauss’s Law

In a laboratory setup, a spherical closed surface is used to measure the net magnetic flux produced

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

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

Maxwell’s Equations – Gauss’s Law

Gauss’s Law is one of Maxwell’s equations and relates the electric flux through a closed surface to

Maxwell's Equations Application

In an electromagnetic system with time-varying fields, consider the implications of Maxwell's equati

Measuring Magnetic Flux Variations

A researcher rotates a coil in a uniform magnetic field to study how the magnetic flux changes with

Oscillations in an LC Circuit

An LC circuit consists of an inductor with inductance $$L$$ and a capacitor with capacitance $$C$$.

Resonant Frequency and Quality Factor of an LC Filter

Design a band-pass LC filter and analyze its performance in terms of resonant frequency and selectiv

Resonant Frequency Variation in an LC Circuit

An LC circuit consists of an inductor with inductance $$L$$ and a variable capacitor with capacitanc

Role of Displacement Current in Maxwell’s Equations

In a charging capacitor, the displacement current plays a significant role in maintaining the contin

Rotating Coil Generator Experiment

A graduate student designs an experiment using a rotating rectangular coil placed in a uniform magne

Self-Inductance of a Solenoid

A solenoid has a length of 0.50 m, a radius of 0.05 m, and 1000 turns.

Sinusoidal EMF from an Alternating Current Generator

A researcher investigates an AC generator where a coil rotates in a magnetic field, producing a sinu

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-Domain Analysis of a Transient LR Circuit

For an LR circuit with a current given by $$I(t)=\frac{V}{R}(1-e^{-\frac{R*t}{L}})$$ after a sudden

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 Efficiency and Core Losses Analysis

A transformer experiment is conducted to determine its efficiency under different load conditions. M

Transformer Efficiency Investigation

This problem examines the relationships in an ideal transformer and explores how various factors aff

Transformer Voltage Regulation Experiment

An experiment is conducted to evaluate a transformer’s voltage regulation by measuring the input vol