AP Physics 2: Algebra-Based FRQ Room

Adjustable Pipe Flow Experiment

In an experiment, water flows through a pipe whose cross-sectional area can be mechanically adjusted

Airflow and Aerodynamic Lift

A researcher investigates the role of airflow in generating lift over an airplane wing using Bernoul

Airflow and Lift on an Airfoil

An airplane wing is designed so that the air above the wing travels at a different speed than the ai

Airflow Over an Airfoil and Lift Generation

In a wind tunnel experiment, an airfoil is subjected to an airflow of $$20\,m/s$$. Pressure sensors

Airfoil Pressure Distribution Study

A series of experiments was conducted in a wind tunnel to measure the pressure distribution along a

Analysis of Buoyant Force on a Submerged Sphere

A solid sphere with a radius of 0.2 m is completely submerged in water (density = $$1000\;kg/m^{3}$$

Analysis of Fluid Flow Measurements in a Laboratory Pipe

A researcher collects flow measurements along a pipe with varying cross-sections. The following data

Analyzing Submerged Structures in Fluids

A marine structure is designed to float partially submerged in a lake. The structure has a total mas

Bernoulli’s Equation and Venturi Meter

A Venturi meter is installed in a pipe to measure fluid flow. The meter provides different pressure

Bernoulli's Equation Application

A horizontal pipe has a constriction such that the cross-sectional area at Section 2 is one-third of

Bernoulli's Equation in a Constricting Pipe

In a pipe system, water is pumped at a constant flow rate. The pipe gradually constricts so that at

Bernoulli's Pressure-Velocity Experiment

An experiment was conducted on fluid flow in a pipe with varying cross-sectional areas. The table be

Bernoulli's Principle in a Constricted Flow System

Water flows through a horizontal pipe that gradually constricts. At point 1, the fluid has a cross-s

Bernoulli’s Principle in Spillway Flow

This problem applies Bernoulli’s principle to analyze water flow over a spillway and to discuss ener

Buoyancy and Archimedes' Principle Investigation

In a laboratory experiment, a researcher investigates the buoyancy of objects using ethyl alcohol (d

Buoyancy and Floating Object

An object with a mass of $$150\;kg$$ and a volume of $$0.75\;m^3$$ is placed in a container filled w

Buoyancy and Floating Object Experiment

An object with a mass of $$150 \; kg$$ and a volume of $$0.75 \; m^3$$ is placed in ethyl alcohol, w

Buoyancy and Floating Objects Analysis

An object with a mass of $$150~kg$$ and volume of $$0.8~m^3$$ is placed in a container filled with a

Buoyancy in Multi-fluid Systems

This problem examines buoyancy when an object is in contact with two immiscible fluids, requiring de

Buoyant Force and Fraction Submerged

An object with a mass of $$150\,kg$$ and a volume of $$0.75\,m^3$$ is placed in a fluid with density

Centrifugal Effects on Fluid Pressure Distribution

A fluid with density $$\rho = 800 \; kg/m^3$$ is contained in a cylindrical container and rotated wi

Column of Oil: Density and Pressure

A vertical column of oil with a density of $$800\;kg/m^3$$ is contained in a cylindrical container w

Continuity and Bernoulli in a River Channel

A river flows from a wide channel into a narrow section. In the wide channel, the cross-sectional ar

Continuity Equation Experimental Variation

The continuity equation predicts that the flow rate in a pipe remains constant. An experiment measur

Continuity Equation in a Non-Uniform Pipe

A researcher is analyzing water flow in a circular pipe whose diameter changes along its length. At

Continuity Equation in Branching Pipes

A pipeline carrying water (density $$1000\;kg/m^3$$) splits into two branches. The main pipe has a f

Continuity Equation: Flow in a Non-uniform Pipe

A circular pipe carries water smoothly. At Point 1, the radius is $$2\,cm$$ with a measured velocity

Density and Hydrostatic Pressure Calculation

A container holds an oil sample with a measured mass of $$1.6$$ kg and a volume of $$2.00 \times 10^

Designing a Pipeline: Balancing Pressure and Flow Rate

An engineering project requires designing a pipeline to transport water over long distances. Changes

Determining Fluid Density

A sample of an unknown liquid has a mass of $$1.2 \times 10^{0} \text{ kg}$$ and occupies a volume o

Diver's Pressure: Hydrostatic and Atmospheric Contributions

A diver descends to a depth of 30 m in seawater with a density of 1025 kg/m³. The atmospheric pressu

Effect of Fluid Density on Buoyancy Force

An object with a fixed volume of $$0.1 \; m^3$$ is fully submerged in two different fluids. Answer t

Examining the Role of Viscosity in Fluid Dynamics Experiments

A researcher is investigating how the viscosity of a fluid affects flow measurements in experiments,

Flow in an Open Channel: Continuity and Energy Considerations

Water flows in an open channel that narrows from a width of 4.0 m to 2.0 m. In the wider section, th

Flow Rate Analysis in Variable Cross-Section Pipes

A water flow experiment is conducted using a pipe with two sections of different diameters. The meas

Flow Rate Variation in a Branching Pipe

A horizontal pipe carrying a total flow rate of $$0.012\,m^3/s$$ splits into two branches. One branc

Flow Regimes: Laminar vs. Turbulent Flow and Continuity Equation

In a fluid dynamics experiment, students observe a smooth transition from laminar to turbulent flow

Fluid Density Analysis

You are provided with a table listing three different fluids along with their measured masses and vo

Fluid Density and Hydrostatic Pressure Calculation

A liquid sample has a mass of $$0.8 \; kg$$ and occupies a volume of $$10^{-3} \; m^3$$. In a separa

Fluid Pressure on a Dam Wall

A civil engineer is evaluating the force exerted on a vertical dam wall by the water in a reservoir.

Force on a Dam from Hydrostatic Pressure

A dam holds back a body of water. The vertical, rectangular face of the dam is 10 m high and 20 m wi

Hydrostatic Pressure and Density Experiment

A researcher conducts an experiment to investigate hydrostatic pressure in two fluids, water and oil

Hydrostatics: Force on Submerged Surfaces

A rectangular plate measuring $$2\,m \times 1\,m$$ is submerged vertically in water (density = 1000

Impact of Temperature on Fluid Density and Pressure

In a controlled experiment, it is observed that a liquid's density decreases by 1% for every 5°C inc

Investigating Air Pressure Changes with Altitude

A researcher measures atmospheric pressure at different altitudes to study its variation with elevat

Measurement Uncertainty in Fluid Density

In a laboratory experiment, the density of an unknown fluid is measured using a pycnometer. The mass

Pressure Calculations in Submerged Structures

A structural engineering team is testing a scale model of a submerged tunnel to study the effects of

Pressure Exerted by Fluid Column

A researcher investigates the variation of pressure with depth in a fluid contained within a transpa

Pressure in a Fluid with Depth-Dependent Density

In a non-uniform fluid, the density varies with depth according to $$\rho(y) = \rho_0 + \alpha y$$,

Pressure Measurements in a Deep Lake

A diver uses a pressure sensor to measure the absolute pressure at various depths in a deep lake. Th

Pressure on Submerged Structures: Dam Windows

A dam features rectangular windows through which engineers measure the pressure exerted by the water

Pump Work Analysis in a Closed Fluid Circuit

In a closed fluid circuit, a pump is used to circulate water so that it maintains a constant flow ra

Relationship Between Pipe Radius and Flow Speed

For an incompressible fluid flowing through a pipe at a constant volume flow rate, the continuity eq

Solar-Powered Water Pump Analysis in a Remote Village

In a remote village, a solar-powered water pump extracts water from a well 20 m deep. The pump must

Solid Column Pressure Calculation

A vertical column made of cement is used in a structural experiment. The column has a uniform cross-

Temporal Flow Rate Analysis from an Experimental Graph

A student records the flow speed of water through a pipe over a 30-second interval. The graph shows

Torricelli’s Law and Fluid Ejection

An open tank at atmospheric pressure contains water (density $$1000\;kg/m^3$$) with a free surface l

Analysis of a P-V Diagram for Isothermal and Adiabatic Processes

This question examines a P-V diagram that displays two distinct thermodynamic processes: one isother

Analysis of Isothermal Process Cycle Using a P–V Diagram

Isothermal processes occur at constant temperature, and the work done can be determined from a P–V d

Analysis of Work Done in Cyclic Processes

In a cyclic thermodynamic process, the net work done by the system is equal to the area enclosed by

Analyzing Energy Balance in a Calorimetry Experiment

In a calorimetry experiment, a water bath is used to measure the energy transfer. The specific heat

Comparative Analysis of Heat Engine Cycles

Two heat engines, Engine A and Engine B, operate under different conditions. Their heat inputs and o

Comparing Thermal Conductivity of Materials

A researcher compares the heat conduction properties of copper and aluminum rods of identical dimens

Conversion between Energy and Work in Cyclic Processes

In a cyclic thermodynamic process, the system converts energy between heat and work. (a) Explain ho

Data Analysis of an Adiabatic Process

An ideal gas undergoes an adiabatic process during which experimental data for pressure and volume a

Determining Heat Engine Efficiency

A cyclic heat engine operates with the following heat transfers during each cycle: it absorbs 1000 J

Deviations of Real Gases from Ideal Behavior

The ideal gas law, $$PV = nRT$$, describes gases under ideal conditions. However, at high pressures

Differentiating Heat Transfer Modes: Convection vs. Conduction

An experiment compares the rate of heat transfer in two different setups: one using a fluid medium (

Effect of Molar Mass on Gas Velocity

The relation $$v_{rms} = \sqrt{\frac{3 * k_{B} * T}{m}}$$ indicates that the molar mass of gas molec

Effects of Mole Number on Gas Pressure

In a series of experiments with a fixed-volume container at constant temperature, the number of mole

Efficiency Evaluation of a Heat Engine: Experimental Design and Data Analysis

Heat engines convert thermal energy into work, but not all the input heat is converted due to ineffi

Entropy Changes in Thermodynamic Processes

A researcher examines a system that undergoes two processes: the system absorbs heat and then reject

Experimental Analysis of Gas Kinetic Energy

In a set of experiments, Maxwell-Boltzmann speed distribution graphs were obtained at different temp

Experimental Test of the First Law of Thermodynamics in an Isobaric Expansion Process

The First Law of Thermodynamics states that $$\Delta U = Q + W$$. Design an experiment to test this

Force on Container Lid from Confined Gas

A cylindrical container has a radius of 15 cm and a height of 30 cm. It contains 0.6 moles of an ide

Gas Pressure Calculation and Net Force Analysis

A 0.8 mole sample of an ideal gas is confined in a cubic container with a side length of 0.5 m at a

Heat Engine Efficiency

A heat engine draws $$800\;J$$ of heat from a high-temperature source and rejects $$450\;J$$ of heat

Heat Engine Efficiency Analysis

A heat engine operates by drawing heat from a high-temperature source and rejecting part of it as ex

Heating a Gas: Conduction vs. Convection

Heat can be transferred via different mechanisms. In the context of a gas being heated, consider the

Investigating Pressure-Temperature Relationship in a Closed Gas Container

In a constant-volume container, the pressure of a confined gas changes as the temperature varies. De

Investigation of Convection Currents in Fluids

A transparent tank filled with water is heated from below. A dye is introduced to visualize the resu

Isothermal Expansion Experiment Error

A student performs an isothermal expansion experiment using a piston-cylinder apparatus immersed in

Isothermal Process and Work Calculation

For an ideal gas undergoing an isothermal process (constant temperature), the work done is given by

Kinetic Energy and Temperature Relationship

An experiment on an ideal gas was conducted to measure the average molecular kinetic energy and temp

Maxwell-Boltzmann Distribution Analysis

The Maxwell-Boltzmann distribution provides a statistical description of the speeds of molecules in

Pressure-Temperature Relationship in a Sealed Container

A sealed container holds an ideal gas at an initial pressure of $$100 \times 10^{3}\;Pa$$ and an ini

Quantifying Radiative Heat Transfer from a Satellite

A satellite in space with a surface area of $$2.0\;m^{2}$$ and an emissivity of 0.85 is operating at

Real Gas Behavior vs. Ideal Gas Law: Experiment Design to Evaluate Deviations

While the ideal gas law (PV = nRT) works well for many gases, real gases deviate from this behavior

RMS Velocity and Temperature Relationship

The root mean square (RMS) velocity of gas molecules is given by $$v_{rms}=\sqrt{\frac{3k_{B}T}{m}}$

Thermal Conductivity through Conduction

An experiment measures the rate of heat transfer through a material using the conduction formula $$\

Thermal Equilibrium and the Zeroth Law

Thermal equilibrium is a key concept in thermodynamics. (a) Define thermal equilibrium and its relat

Thermodynamic Processes and Energy Changes

Many thermodynamic processes involve changes in volume, pressure, and temperature. Consider an ideal

Time-Resolved Thermal Imaging Experiment Error

A student uses a thermal imaging camera to study the cooling rates of a heated brick as it returns t

Understanding Temperature Scales in Thermodynamic Calculations

A student records a room temperature of 25°C for an experiment.

Verification of RMS Speed Dependence on Temperature

An experiment measured the RMS speed of gas molecules at different temperatures, with the following

Analysis of Equipotential Maps and Electric Field Lines

Consider a dipole formed by two equal but opposite point charges. Analyze the relationship between e

Capacitance Measurement via Frequency-Dependent Response

A student performs an experiment to determine the capacitance of a capacitor by analyzing its respon

Capacitor: Potential Difference and Energy Storage

In this problem you will analyze a parallel-plate capacitor by calculating its potential difference

Charge Transfer and Work Calculation

Consider a system where two fixed charges create an electric potential difference between two points

Coulomb’s Law in Different Media

A study investigates how the presence of various media affects the force between two point charges,

Coulomb’s Pendulum Experiment Error Analysis

In an experiment designed to measure the electrostatic force between two identically charged spheres

Dipole Field Analysis

An electric dipole is formed by two point charges, $$+Q$$ and $$-Q$$, where $$Q = 4.0 \times 10^{-9}

Distance Dependence in Coulomb's Law

Coulomb's Law quantitatively describes the force between two point charges as inversely proportional

Effect of Plate Separation on Capacitance in a Parallel-Plate Capacitor

A parallel-plate capacitor is constructed with plates of area A = 0.02 m². The separation between th

Effect of Temperature on Dielectric Constant in Capacitors

Propose an experimental setup to study how temperature affects the dielectric constant of a capacito

Electric Dipole Field Analysis

A dipole is composed of two point charges, $$+Q$$ and $$-Q$$, each of magnitude $$4.0\;nC$$, separat

Electric Field from Multiple Point Charges

This question involves computing the net electric field at a specific point due to three point charg

Electric Potential Energy Conversion in a Charged Projectile Experiment

An experiment is conducted to analyze the conversion of electrical potential energy into kinetic ene

Electric vs. Gravitational Forces in a Hydrogen Atom

Consider a hydrogen atom where the proton (charge $$+e$$) and electron (charge $$-e$$) are separated

Energy Storage in a Parallel-Plate Capacitor

A parallel-plate capacitor has a capacitance of 10 nF and holds a charge of 50 μC on each plate. (a

Force Balance in a Uniform Electric Field

A researcher studies a small object of mass $$5 \; g$$ in a vertical, uniform electric field produce

Force Comparison in Hydrogen Atom

An experiment is conceptually designed to compare the magnitude of the electric force to the gravita

Fringing Fields in Parallel-Plate Capacitors

In a real parallel-plate capacitor, the electric field near the edges deviates from the ideal unifor

Influence of Charge Magnitude on Electric Potential

Design an experiment using a variable charge on a point charge source to measure the resulting elect

Kinetic Energy Gain from Electrical Potential Energy Change

A fixed charge \(q_1 = +2 \times 10^{-6} \; C\) and a mobile charge \(q_2 = -1 \times 10^{-8} \; C\)

Mapping Electric Field Around a Point Charge

Design an experiment to map the electric field in the vicinity of a point charge using a test charge

Mapping Equipotential Surfaces in a Non-uniform Electric Field

In a region of space, the electric potential has been measured at various distances from a fixed cha

Measurement and Analysis of Charge Distribution on a Sphere

A non-conducting sphere of radius 5 cm carries a total charge of 2×10⁻⁸ C uniformly distributed thro

Motion of a Charged Particle in a Uniform Electric Field

A small charged particle with charge q = 2.0×10^-6 C and mass m = 2.0×10^-3 kg is released from rest

Motion of a Charged Particle in Combined Electric and Gravitational Fields

A charged particle has a mass of $$2.0*10^{-3}$$ kg and a charge of $$+1.0*10^{-6}$$ C. It is releas

Net Electric Force in a Square Configuration

Four identical positive point charges, each of $$2.0 \times 10^{-9} \; C$$, are placed at the vertic

Net Electric Force on a Central Charge in a Square Configuration

Four equal positive point charges are fixed at the vertices of a square, and a negative point charge

Parallel-Plate Capacitor: Potential Difference and Plate Area

A parallel-plate capacitor stores a charge of 50 μC on each plate and has a capacitance of 10 nF. (

Potential Difference in a Parallel-Plate Capacitor

A parallel-plate capacitor has plates of area A = 0.05 m² separated by a distance d = 0.001 m and is

Potential Energy Change in a Non-Uniform Field

A test charge moves in the electric field of a fixed point charge. Using the concept of electric pot

Superposition of Forces in a Square Configuration

Four equal positive point charges are placed at the vertices of a square. A negative charge is place

Surface Charge Distribution on Irregular Conductors

The distribution of surface charge on conductors is influenced by the geometry of the surface. This

Work and Change in Electric Potential Energy in a Uniform Field

A positive test charge of $$q = +2.0 \times 10^{-6}\,C$$ is moved a distance of $$0.05\,m$$ in the d

Work Required to Assemble a Triangular System of Point Charges

Three point charges are fixed in place forming a triangle. The charges and separations are: Q₁ = +2.

Analysis of Ammeter and Voltmeter Placement

This question addresses the proper usage of ammeters and voltmeters in a circuit for accurate measur

Analysis of Current Flow in a Circuit with Mixed Components

An experiment involves a circuit that includes a combination of resistors and a capacitor branch. Th

Analyzing Capacitors in Series and Parallel

Two capacitors with capacitances of 4 μF and 6 μF are used in a circuit.

Basic Circuit Analysis

A 9V battery is connected in a simple circuit containing a single resistor of 10 Ω. Using Ohm’s Law

Battery Internal Resistance and Terminal Voltage Analysis

A battery can be modeled as an ideal electromotive force (EMF) in series with an internal resistance

Battery Internal Resistance: Terminal Voltage Measurement

A battery with an ideal electromotive force (EMF) of 9 V is connected to a resistor of 10 Ω. Due to

Capacitor Combinations and Equivalent Capacitance

A circuit contains three capacitors with the following capacitances: 4 μF, 6 μF, and 12 μF. In the c

Capacitor Energy Storage and Discharge Efficiency

A capacitor with a capacitance of 10 μF is charged to 12 V and then discharged through a load. The t

Capacitor Modification in an RC Circuit

A capacitor in an RC circuit is initially charged to a voltage $$V_0$$, storing a charge $$Q = C_0 *

Capacitors in Series and Parallel: Equivalent Capacitance Analysis

An experiment is performed using two identical capacitors each with capacitance $$C = 5\;F$$. They a

Charging Behavior of an RC Circuit

A capacitor with capacitance $$C = 5 \text{ F}$$ is charged through a resistor of $$R = 3 \Omega$$ b

Comparative Analysis of Series and Parallel Circuit Configurations

In an experiment, two circuit configurations are tested: one with resistors arranged in series and o

Complex Circuit Analysis Using Kirchhoff's Laws

A 12 V battery is connected to a circuit where a resistor of 4 Ω is in series with a parallel combin

Designing a Circuit for a Specific Equivalent Resistance

You are provided with resistors of values 50 Ω, 100 Ω, 200 Ω, and 400 Ω. Your task is to design a ci

Designing an Experiment to Measure Current in a Complex Circuit

Propose an experimental procedure to measure the current distribution in a complex circuit containin

Determining Capacitance Changes Due to Physical Adjustments

A parallel-plate capacitor has plate area A, plate separation d, and a dielectric constant k. Answer

Determining Resistivity of Various Materials

Resistance (R) and resistivity (\(\rho\)) are related by the expression $$R = \rho*\frac{l}{A}$$. Yo

Discharging of a Capacitor in an RC Circuit

A capacitor initially charged to $$12 \text{ V}$$ is discharged through a resistor of $$4 \Omega$$.

Electromotive Force and Terminal Voltage under Load

This problem explores the relationship between a battery's true electromotive force (EMF), its inter

Energy Storage Analysis in Capacitors

A capacitor stores energy according to the formula $$E = \frac{1}{2} C V^2$$. Consider a capacitor w

Exploring the Concepts of Internal Resistance and Circuit Efficiency

A study claims that batteries with lower internal resistance operate more efficiently, resulting in

Impact of Resistor Network Configuration on Circuit Performance

A circuit is composed of a resistor network where two $$8 \Omega$$ resistors are connected in series

Investigating Current Division in a Parallel Resistor Network

A student sets up a circuit in which two resistors, one 10 Ω and one 20 Ω, are connected in parallel

Investigating the Effect of Capacitor Dielectric Constant on Capacitance

In a laboratory experiment, capacitors are built using different dielectric materials. The capacitan

Investigating the Impact of Wire Geometry on Electrical Resistance

A claim is made that the resistance of a wire depends on its length and cross-sectional area as desc

Measuring Electric Current and Voltage in a Simple Circuit

In a simple circuit consisting of a battery, a resistor, and connecting wires, you are asked to inve

Measuring Power Dissipation in Resistive Elements

Power dissipation in a resistor is an important factor for both performance and safety. Given the fo

Multi-branch Circuit Analysis

A complex circuit consists of two branches: Branch A contains two resistors (4 Ω and 3 Ω) in series,

Non-Ohmic Behavior in Real-World Devices

Some devices, such as filament bulbs or semiconductors, exhibit non-ohmic behavior, meaning their V-

Ohm's Law Application to Resistivity Measurement

A uniform wire of length 2 m and cross-sectional area $$1 \times 10^{-6} m^2$$ has a measured resist

Power Dissipation in Circuit Components

A simple circuit consists of a resistor connected to a battery. Consider a scenario where a 9 V batt

Power Dissipation in Resistive Circuits

A resistor with a resistance of $$10\,\Omega$$ is connected to a $$9\,V$$ battery. Answer the follow

RC Circuit Capacitor Charging

A capacitor is connected in series with a resistor and a battery in an RC circuit. Answer the follow

RC Circuit Response and Steady State Behavior

Consider an RC circuit containing a battery, a resistor, a capacitor, and an additional resistor in

RC Circuit Response to Voltage Change

Consider an RC circuit consisting of a resistor of $$100\,\Omega$$ and a capacitor of $$100\,\mu F$$

Resistor Networks and Equivalent Resistance

A circuit contains three resistors arranged in a mixed series-parallel configuration. Resistors R1 =

Series and Parallel Resistor Networks

Consider a circuit that contains a 12 V battery connected to three resistors arranged such that resi

Transient Analysis with Switch Operation in RC Circuits

An RC circuit consists of a $$10~V$$ battery, a resistor of $$500~\Omega$$, and a capacitor of $$200

Transient Response Analysis in an RC Circuit at Switch Closure

An RC circuit is suddenly closed (switch closed), resulting in a rapid change in current through the

Wire Resistance Calculation

A platinum wire has a length of $$2\,m$$ and a radius of $$1\,mm$$. Given the resistivity of platinu

Analysis of Solenoids: Field Uniformity and Enhancements

The performance of a solenoid as an electromagnet depends on its design. Investigate the factors inf

Angular Dependence of Magnetic Force

A series of experiments measures the magnetic force on a charged particle moving in a constant magne

Assessing Iron Dust Experiments for Bar Magnets

A study uses iron dust to demonstrate that the magnetic field inside a bar magnet is continuous and

Compass Mapping of Bar Magnet Field

In an experiment, a bar magnet is used to map its magnetic field by measuring the deflection angle o

Current-Carrying Wire Magnetic Field

A researcher examines the magnetic field created by a long, straight current-carrying wire. The magn

Design and Analysis of a Railgun

Railguns use magnetic forces to accelerate projectiles. In this problem, analyze the principles behi

Effect of Magnetic Field Strength on Induced Current

Design an experiment to explore how varying the magnetic field strength affects the induced current

Energy Conversion in an Electromagnetic Generator

A simple electromagnetic generator consists of a rotating loop placed in a uniform magnetic field, r

Energy Transformation in a Moving Conductor Experiment

In an experiment, a conducting bar is made to slide through a uniform magnetic field, generating an

Faraday’s Law and Rotating Loop

A circular loop rotates in a uniform magnetic field, inducing an emf according to Faraday’s Law. Ana

Force on a Current-Carrying Wire in a Magnetic Field

A straight wire carrying an electric current is placed in a uniform magnetic field. Answer the follo

Force on a Moving Charge

This FRQ focuses on calculating the magnetic force on a moving charge and interpreting its direction

Force on Wire and Its Dependence on Current

An experiment measures the magnetic force on a current-carrying wire in a fixed magnetic field for d

Graph Analysis: Magnetic Force vs. Velocity

An experiment investigates the relationship between the velocity of a charged particle and the magne

Graphical Analysis of Magnetic Flux Change

This FRQ involves analyzing experimental data on magnetic flux change over time, determining the ind

Induced EMF and Conductor Length

An experiment is conducted in which a conducting rod moves through a magnetic field, and the induced

Induced EMF in a Loop with Time-Varying Magnetic Field

A circular loop with a constant area of $$A = 0.02 m^2$$ is placed in a magnetic field that increase

Induced EMF in a Rotating Square Loop Experiment

A laboratory experiment involves a square loop of wire that rotates at a constant angular speed in a

Induced EMF in a Sliding Rod Circuit

Consider a circuit formed by a sliding rod of length $$\ell$$ that moves on conducting rails, comple

Lenz’s Law and Induced Current Direction

In an experiment, a coil is subjected to a changing magnetic flux by moving a magnet toward and then

Lenz's Law in a Sliding Bar Circuit

A conducting bar slides on a pair of parallel rails, forming a rectangular loop, in the presence of

Magnetic Field Diagram Analysis

Examine the provided diagram of a bar magnet's magnetic field. The diagram shows a bar magnet labele

Magnetic Field Mapping with Iron Filings

Permanent magnets produce complex magnetic fields that can be visualized using iron filings. In this

Magnetic Field Visualization

This FRQ explores the nature of magnetic fields and how magnetic field lines are used to represent t

Magnetic Flux and Loop Angle

A circular loop of wire is placed in a uniform magnetic field. Its orientation relative to the field

Magnetic Force on a Moving Charge

A charged particle moves through a uniform magnetic field. Use the relationship that the magnetic fo

Magnetic Levitation and Force Equilibrium

Investigate the conditions required for magnetic levitation using magnetic repulsion, and analyze po

Magnetic Torque on a Current Loop

A rectangular loop of wire with length $$L = 0.1 \; m$$ and width $$w = 0.05 \; m$$ carries a curren

Mapping Magnetic Field Lines of a Bar Magnet

In this experiment, a researcher uses iron filings sprinkled on a sheet of paper placed atop a perma

Mapping Magnetic Field Lines using Iron Filings

Design an experiment to map the magnetic field lines around a bar magnet using iron filings. Your de

Mapping Magnetic Field Lines with Iron Dust

A recent experimental report claims that by sprinkling iron dust on a piece of paper placed over a b

Measurement of Induced Current in a Transformer Experiment

A group of students builds a simple transformer and measures the induced current in the secondary co

Motional EMF Analysis

A researcher moves a conducting rod of length $$\ell = 0.5 m$$ through a uniform magnetic field of s

Motional EMF and Conductor Velocity

A lab simulation studies the effect of a conducting rod's velocity on the motional EMF generated whe

Motional EMF in a Conducting Rod

This FRQ focuses on the phenomenon of motional electromotive force (emf) generated in a moving rod w

Motional EMF in a Moving Conductor

A conducting rod of length 0.5 m moves at a constant velocity of 3 m/s perpendicular to a uniform ma

Net Force on a Current-Carrying U-shaped Wire

Consider a U-shaped wire immersed in a uniform magnetic field of magnitude $$B = 0.2 \; T$$ directed

Qualitative Analysis of Magnetic Field Lines Using Iron Dust Technique

A scientist uses finely milled iron dust to visualize the magnetic field lines around a permanent ba

Rotating Coil Induced Current

A coil consisting of N turns and area A rotates in a uniform magnetic field of strength B with a con

Sinusoidal Induced EMF in a Rotating Loop

A circular loop of radius 0.1 m rotates in a uniform magnetic field of 0.25 T with a constant angula

Time-Dependent Induced EMF in a Rotating Loop

Design an experiment to investigate how the induced emf in a rotating loop varies over time, particu

Uniform Field of a Solenoid

A researcher studies the magnetic field produced by a solenoid. Measurements of the magnetic field a

Analysis of Polarization and Malus' Law

This question explores the concept of polarization, quantitative analysis using Malus' law, and requ

Calculating Lens Power from Image Magnification

The power of a lens is defined as the reciprocal of its focal length (in meters). Analyze an example

Coherence in Interference Patterns

A student compares the interference patterns produced by a coherent laser light source and an incohe

Comprehensive Analysis of Optical Imaging Systems

Design an experiment that integrates lenses and mirrors to project an image onto a screen. This comp

Concave Mirror Image Formation

An object of height 5 cm is placed 20 cm from a concave mirror with a focal length of 10 cm. Answer

Convex Mirror Image Analysis

Convex mirrors produce images that are always virtual, diminished, and upright. This question requir

Convex Mirror Image Formation

An object of height $$5 \text{ cm}$$ is placed $$20 \text{ cm}$$ in front of a convex mirror with a

Diffraction Gratings and Spectral Analysis

A diffraction grating is used to analyze the spectral composition of a light source. A graph showing

Diverging Lens Image Characteristics

An object of height $$h_o = 11 \ cm$$ is placed at a distance of $$d_o = 48 \ cm$$ in front of a div

Diverging Thin Lens Analysis

A researcher examines a diverging lens with a focal length of $$-20$$ cm. An object of height 8 cm i

Double Slit Interference Analysis: Fringe Positions

In a Young's double slit experiment, light of wavelength $$589*10^{-9}$$ m passes through two slits

Image Formation by Convex Mirrors

A convex mirror has a focal length of $$20\,cm$$. An object is placed $$30\,cm$$ in front of the mir

Lens Power Calculation from Image Magnification

A student uses a converging lens to investigate magnification. In the experiment, an object is place

Optical Instrument Design: Telescope Model

A researcher is designing a simple astronomical telescope that employs a converging objective lens a

Oscillating Charges and the Generation of EM Waves

An oscillating charge is a fundamental source of electromagnetic radiation. This problem involves ex

Photon Energy Calculation in the Electromagnetic Spectrum

This question involves using fundamental relations in quantum physics to calculate the energy of pho

Plane Mirror Image Formation

An object is placed 25 cm in front of a plane mirror. (a) Determine the distance of the image from

Plane Mirror Image Formation and Analysis

Plane mirrors reflect light according to the law of reflection and produce images that are virtual a

Plane Mirror Reflection: Image Formation Error Analysis

A student designs an experiment to study image formation using a plane mirror. The setup involves an

Polarization and Brewster's Angle

When unpolarized light strikes a glass surface, the reflected light becomes partially polarized. Con

Polarization and Electromagnetic Wave Behavior

In an experiment testing polarization, a polarizer is rotated and the transmitted light intensity is

Polarization and Intensity of EM Waves

A beam of unpolarized light passes through a polarizing filter, emerging as linearly polarized light

Radiation Pressure and Electromagnetic Waves

An experiment measures the force exerted on a surface by electromagnetic radiation at various light

Radio Wave Wavelength Determination

A radio transmitter emits electromagnetic waves with a frequency of $$f = 100*10^{6} \ Hz$$.

Ray Tracing for Converging Lenses and Mirrors

This question involves constructing ray diagrams for optical instruments. (a) Draw and label a ray

Reflection and Refraction in a Glass Slab

A student investigates the behavior of a light beam as it passes from air into a flat glass slab wit

Refraction and Snell's Law Experiment

A light beam traveling in air (index of refraction $$n_1=1$$) strikes a glass surface (index of refr

Single Slit Diffraction Analysis

A single slit diffraction experiment is performed with a slit width of $$a = 0.1 * 10^{-3}$$ m, a sc

Single-Slit Diffraction: Experimental Error Analysis

In an experiment aimed at studying single-slit diffraction, a student sets up a coherent light sourc

Thin Diverging Lens Image Formation

An object of height 12 cm is placed 30 cm from a diverging lens with a focal length of -20 cm. Answe

Thin Diverging Lens Imaging

A diverging lens with a focal length of -15 cm is used to form an image of an object 9 cm tall place

Thin Film Interference

A thin film of oil (index $$n = 1.25$$) rests on water (index $$n = 1.33$$). White light is incident

Total Internal Reflection at Air-Water Interface

Light traveling within water (with an index of refraction $$n_{water} \approx 1.33$$) approaches the

Total Internal Reflection in Optical Fibers

A set of experiments investigates the conditions under which total internal reflection (TIR) occurs

Total Internal Reflection in Optical Fibers

An optical fiber has a core with an index of refraction of 1.50 and a cladding with an index of 1.40

Total Internal Reflection: Critical Angle Error Analysis

In an experiment intended to determine the critical angle for total internal reflection at the water

Two-Lens System Analysis

A compound optical system consists of a converging lens with a focal length of 20 cm and a diverging

Photoelectric Experiment: Variation with Intensity

A researcher conducts a photoelectric experiment on a sodium surface with a work function of $$2.28\

Wave-Particle Duality Experiment with Electrons

An experiment is conducted in which electrons are accelerated through a potential difference and the