AP Physics 2: Algebra-Based FRQ Room

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 and Lift over an Aerofoil

This problem explores how differences in air velocity over and under an airplane wing create lift, u

Application of Bernoulli's Equation

In a horizontal pipe, a pump forces water (density $$1000\;kg/m^3$$) from point 1 into a constricted

Average Hydrostatic Pressure on a Submerged Plate

A rectangular plate measuring 2 m in width and 1.5 m in height is submerged vertically in water (den

Bernoulli's Equation in a Horizontal Pipe

A horizontal pipe carries water and gradually narrows. In the wide Section 1 (diameter 8 cm), the wa

Bernoulli's Equation in Constricted Flow

Water flows through a horizontal pipe that gradually narrows. At Point 1, the cross-sectional area i

Bernoulli's Principle in a Venturi Tube

A Venturi tube is installed in a horizontal pipe. At section 1 the cross-sectional area is $$A_1$$ a

Bernoulli's Principle in Lift Generation

Aircraft wings generate lift in part due to differences in airspeed above and below the wing. (a) Ex

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

Buoyant Force in Varied Fluids

A solid object with a mass of $$200 \; kg$$ and a volume of $$0.5 \; m^3$$ is immersed in three diff

Buoyant Force Measurement Experiment

In an experiment designed to measure buoyant force, the weights of submerged objects were recorded.

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

Comparing Flow Rates in Different Pipes

A fluid flows through a pipe system that splits into two branches. Branch A has a circular cross-sec

Density Variation in Immiscible Fluids

An object is submerged partly in oil and partly in water. A table provides mass and volume data for

Density Variation with Temperature in Liquids

A researcher measures the density of water at different temperatures and obtains the following data:

Designing a Pipeline: Balancing Pressure and Flow Rate

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

Designing a Stable Floating Vessel

You are tasked with designing a small boat to float on water (density $$1000\,kg/m^3$$). The boat ha

Designing a Water Fountain: Pressure and Flow

A landscape architect is designing a water fountain and needs the water jet to reach a maximum heigh

Designing an Experiment to Validate the Continuity Equation

An engineering team aims to validate the continuity equation for an incompressible fluid flowing thr

Determining Buoyant Force on a Partially Submerged Object

A physics student examines the buoyant force experienced by an object when it is partially submerged

Determining Object Volume through Fluid Displacement

A student in a laboratory measures the volume of an irregularly shaped stone by submerging it in wat

Effect of Temperature on Fluid Density and Hydrostatic Pressure

Design an experiment to measure how the density of a fluid changes with temperature and how these ch

Effect of Temperature on Fluid Density and Pressure in a Closed System

A thermal engineer investigates how an increase in temperature affects the density of water and, con

Energy Conservation in Fluid Flow: Laminar vs. Turbulent Regions

In a horizontal pipe, regions of laminar and turbulent flow are observed. Pressure and velocity meas

Experimental Analysis of Lift Generation

In wind tunnel experiments, an airfoil is tested under varying flow speeds. A table gives measured d

Exploration of Hydrostatic Pressure in a Dam Wall

A dam holds back a reservoir of water with a density of $$1000~kg/m^3$$. Consider the dam's vertical

Floating Object in Stratified Fluids

An object with a volume of 0.5 m³ and a density of 850 kg/m³ is placed in a container holding two im

Flow Rate Conundrum in a Diverging-Nozzle Experiment

A diverging-converging nozzle experiment reports that increasing the nozzle diameter leads to a decr

Fluid Flow in a River: Application of the Continuity Equation

A field study of a river involves measuring water flow through sections of differing cross-sectional

Fluid Flow Over an Airfoil

Airflow over an airplane wing creates pressure differences that result in lift. Using Bernoulli's eq

Fluid Flow Through an Orifice

A large tank drains water through a small orifice at its bottom. According to Torricelli’s law, the

Hydrostatic Pressure and Density Experiment

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

Impact of Fluid Density on Buoyancy Forces

A block of wood with a volume of 1.0 m³ and a density of 600 kg/m³ floats in freshwater (density 100

Industrial Fluid Density and Pressure Calculation

A researcher in an industrial laboratory is studying fluid properties for engineering applications.

Investigating Fluid Viscosity Effects on Flow

Fluid viscosity plays a significant role in determining flow characteristics. High viscosity fluids

Investigating Temperature Dependence of Fluid Density

The density of a liquid changes with temperature. A table below provides measurements of density at

Measuring Hydrostatic Pressure in an Underwater Environment

An oceanographer sets up an experiment to measure the hydrostatic pressure as a function of depth in

Modeling Fluid Flow in a Conical Pipe

Consider a conical pipe whose radius decreases linearly with distance x according to $$r(x) = r_0 -

Open Channel Pressure Measurement

In an open channel flow experiment, gauge pressures were measured at different depths below the free

Optimization of Fluid Flow in Industrial Piping Systems

An industrial piping system includes a segment where the pipe narrows from a diameter of 0.3 m to a

Pipe Flow and the Continuity Equation Experiment

A student is investigating fluid flow through a pipe whose diameter varies along its length. The hyp

Pressure at an Interface of Two Fluids

A container holds two immiscible fluids. A layer of oil (density $$800\;kg/m^3$$, depth $$0.5\;m$$)

Pressure Changes with Altitude

Atmospheric pressure decreases with altitude. A graph shows measured pressures at various altitudes.

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

Quantitative Analysis of Pressure Distribution in an Accelerating Fluid

A rectangular container with a length of $$2 \cdot m$$ is filled with water (density = $$1000 \cdot

Relationship Between Pipe Radius and Flow Speed

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

Solid Column Pressure Calculation

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

Static Fluid Pressure in a Tank

A cylindrical tank is filled with water (density $$\rho = 1000 \; kg/m^3$$). Consider a point locate

Venturi Meter Experiment: Applying Bernoulli's Principle

Design an experiment using a Venturi meter to measure fluid flow speed and to test Bernoulli's princ

Viscosity Impact on Pipe Flow Rates

An experiment was conducted to investigate the effect of fluid viscosity on flow rates in identical

Wind Tunnel Dynamic Pressure Measurement Error

A student performs an experiment in a wind tunnel to measure dynamic pressure using a pitot tube. Th

Adiabatic Expansion and Temperature Change

An ideal diatomic gas undergoes an adiabatic expansion. For such a process, the relation $$T*V^{\gam

Adiabatic Process Analysis

In an adiabatic process, no heat is exchanged with the surroundings. (a) Define an adiabatic process

Adiabatic Process Calculations

An ideal gas undergoes an adiabatic expansion, meaning that no heat is exchanged with the surroundin

Adiabatic vs. Isothermal Transition Timing Experiment Error

A student designs an experiment to compare adiabatic and isothermal expansions of a gas by rapidly m

Analysis of Atmospheric Pressure and Gas Density

Explain why the high pressure generated by confined gas does not cause the container lid to pop off,

Analysis of Thermodynamic Processes on a P–V Diagram

A researcher examines four thermodynamic processes (isothermal, adiabatic, isobaric, and isochoric)

Analyzing Deviations from the Ideal Gas Law

A researcher measures the pressure of a gas at various volumes and observes deviations from the Idea

Application of the First Law in Gas Expansion

A researcher studies an isobaric expansion of a gas. During the process, the gas absorbs $$250\,J$$

Chemical Reaction Calorimetry Experiment Error

A student carries out a calorimetry experiment to determine the heat released during an exothermic c

Combined Thermodynamic Processes

A gas initially at state A \((P = 2.0\times10^5 \text{ Pa}, V = 0.01 \text{ m}^3, T = 300 \text{ K})

Comparing Real and Ideal Gas Behavior

Discuss the limitations of the Ideal Gas Law and explain the necessary corrections for real gases us

Comparison of Isothermal and Adiabatic Processes

A gas transitions between the same initial and final states via two different paths: one is isotherm

Conduction Heat Transfer: Experimental Design for Material Thermal Conductivity Measurements

Heat conduction through materials depends on their thermal conductivity. Design an experiment to mea

Convection Currents Measurement Experiment Error

A student investigates convective heat transfer in a container of water by heating a plate at the bo

Convection Versus Conduction in Fluid Heating

In a laboratory experiment, two identical metal cylinders are heated on their sides. One cylinder co

Derivation and Calculation of RMS Speed

The root-mean-square (RMS) speed of gas molecules is given by the formula $$v_{rms} = \sqrt{\frac{3\

Designing a Convection Experiment

Develop an experimental proposal to investigate how fluid temperature affects the rate of convective

Designing an Experiment to Measure Convective Heat Transfer

A researcher aims to measure the convective heat transfer coefficient in a fluid flowing over a heat

Determining Heat Engine Efficiency

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

Effect of Temperature on rms Velocity

An experiment is conducted to investigate how changes in temperature affect the root mean square (rm

Efficiency of a Refrigeration Cycle

A refrigerator operates between a cold reservoir at $$280\;K$$ and a warm reservoir at $$300\;K$$.

Entropy Change and the Second Law of Thermodynamics

During a reversible isothermal expansion of an ideal gas, the entropy change is described by the equ

Entropy Change in a Heating Process

An ideal gas (1 mole) undergoes a reversible isobaric process in which its temperature increases fro

Entropy Change in a Thermodynamic Cycle

During a cyclic process, an experiment measures the change in entropy during various stages. Analyze

Entropy Changes in Thermodynamic Processes

Consider an ideal gas that undergoes an isothermal expansion from an initial volume $$V_1$$ to a fin

Evaluating a Cooling System's Efficiency

A refrigerator extracts 500 J of heat from its interior and requires 150 J of work input per cycle.

Evaluating Experimental Error in the Ideal Gas Law Measurements

A laboratory experiment uses measured values of pressure, volume, and temperature to calculate the n

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

Exploring Adiabatic Cooling and Heating in Atmospheric Processes

Adiabatic processes are crucial for understanding weather phenomena. When air parcels rise, they exp

Exploring Kinetic Molecular Theory via Maxwell-Boltzmann Distribution

An experiment is conducted to study the speed distribution of gas molecules. The data is represented

First Law in a Cyclic Process

A closed system undergoes a cyclic process involving isothermal, isobaric, and adiabatic steps. Answ

Force on a Container Lid

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

Gas Diffusion and Molecular Speed Distribution

The rate of diffusion in gases is significantly influenced by the molecular speed distribution. (a)

Heat Engine Efficiency and Energy Analysis

A heat engine operates between a high-temperature reservoir at $$T_H = 650\;K$$ and a low-temperatur

Heat Transfer by Radiation

Unlike conduction and convection, heat transfer by radiation involves electromagnetic waves. (a) Wri

Heat Transfer Conduction/Convection Experiment Error

A student investigates heat transfer through a metal rod by heating one end and measuring temperatur

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

Investigating Temperature and Pressure Effects on Gas Behavior

In a laboratory experiment, gas pressures were measured at various temperatures while keeping the vo

Investigating Thermodynamic Processes: Isobaric vs Isochoric

In a controlled experiment, a gas undergoes two distinct processes: an isobaric expansion followed b

Investigation of Pressure in Confined Gases

A researcher conducts an experiment using a sealed, rigid container fitted with a pressure sensor to

Isothermal vs. Adiabatic Processes

In a laboratory experiment, a gas is compressed in a piston under two different conditions: one proc

Maxwell-Boltzmann Distribution Analysis

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

Net Force on a Confined Gas Container Lid

A cylindrical container holds gas at an internal pressure of $$1.018 \times 10^5\,Pa$$, while the ex

Non-Ideal Gas Behavior and Real Gas Equations

A researcher observes that at high pressures, real gases deviate from ideal behavior. To account for

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

Reversibility and Work in Thermodynamic Cycles

A reversible thermodynamic cycle is performed, and a P–V diagram of the cycle is recorded. Use the d

RMS Velocity and Temperature

The RMS (root-mean-square) velocity of molecules in an ideal gas is given by $$v_{rms} = \sqrt{\frac

Statistical Interpretation of Gas Behavior

The kinetic theory of gases connects microscopic molecular behavior with macroscopic properties. Two

Testing Thermal Equilibrium: The Zeroth Law

An experiment is conducted to verify the Zeroth Law of Thermodynamics using three objects: A, B, and

Thermodynamics and Mechanical Work in an Automobile Engine

An internal combustion engine converts the chemical energy of fuel into mechanical work. Consider th

Understanding Thermal Equilibrium and the Zeroth Law

The Zeroth Law of Thermodynamics states that if object A is in thermal equilibrium with object B, an

Work and Internal Energy in an Isochoric Process

A gas is contained in a rigid, fixed-volume container. During a heating process, the pressure of the

Work Done Along Different Thermodynamic Paths

Consider a gas that changes state from a to b via two different paths. Path 1: An isobaric expansion

Analyzing Electric and Gravitational Forces in a Hydrogen Atom

In a hydrogen atom, the proton has a mass of $$1.6 \times 10^{-27} \; kg$$ and a charge of $$+e$$, a

Balancing Gravitational and Electric Forces

A small object of mass 5 g is placed at a distance of 2 cm above a large positively charged plate, w

Capacitor Discharge and RC Time Constant

A capacitor with capacitance 20 μF is charged to 120 V and then allowed to discharge through a resis

Capacitor: Potential Difference and Energy Storage

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

Charge Quantization Experiment Analysis

An experiment measures the charge on small spheres, and the measured values (in Coulombs) are found

Charged Oil Drop Experiment: Uniform Field and Drag Force Error

In a modified oil drop experiment intended to verify the quantization of electric charge, tiny oil d

Charged Projectile Motion: Vector Decomposition Error

An experiment is set up to study the trajectory of a charged projectile launched horizontally in the

Charging Methods Experiment: Conduction vs. Induction

This experiment compares two methods of charging an object: conduction and induction. Two identical

Comparative Analysis: Charging by Conduction vs. Induction

A metal sphere is charged using two distinct methods: conduction and induction. Compare the processe

Coulomb’s Law in Different Media

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

Deriving Capacitance from Physical Dimensions

A parallel-plate capacitor is constructed with a plate separation $$d$$ and plate area $$A$$ in vacu

Dielectric Effects on Capacitor Behavior

A parallel-plate capacitor initially has a vacuum between its plates and is charged to a voltage V₀.

Dipole Electric Field at Midpoint

A dipole is formed by two point charges of +4.0 nC and -4.0 nC separated by a distance of 6.0 cm. De

Effects of Dielectrics on Capacitor Performance

A capacitor with an initial capacitance $$C_0$$ has a dielectric material with a dielectric constant

Electric Charge Distribution on Conductors: Capacitance Influence Error

In an experiment aimed at studying charge distribution, two metallic spheres of different radii are

Electric Dipole Analysis in a Uniform Medium

An electric dipole is formed by two point charges, +4.0 nC and -4.0 nC, separated by 6.0 cm in air.

Electric Field from an Infinite Charged Sheet

Consider a large sheet with a uniform surface charge density σ = 1.5 × 10⁻⁶ C/m².

Electric Field Mapping Using Discrete Data Points

A student conducts an experiment to measure the electric field around a set of point charges by firs

Electric Field on the Axis of a Charged Ring

A thin circular ring of radius $$R = 0.15\,m$$ carries a uniformly distributed total charge of $$Q =

Electric Potential Difference in a Radial Field

A point charge Q = 1.0 × 10⁻⁹ C produces an electric field in space. A test charge is moved from poi

Electric Potential Due to a Point Charge

Given a point charge Q = 2×10⁻⁹ C, determine the electric potential at a point located 2 cm from the

Electric Potential Due to Multiple Charges

Consider two point charges: $$Q_1 = +2 \times 10^{-9} \; C$$ located at \((-0.04 \; m, 0)\) and $$Q_

Electric Potential from Multiple Point Charges

Two fixed point charges, $$Q_1$$ and $$Q_2$$, are located at specified positions. A point A is locat

Electric Potential in a Dipole Configuration

An electric dipole is formed by two charges +Q and -Q with Q = 5.0 × 10⁻⁹ C, separated by 8.0 cm. Co

Electric Potential Variation Analysis

A series of electric potential measurements were taken at three different positions (A, B, and C) in

Electrostatic Shielding and Induced Charges on a Conducting Shell

A hollow, spherical, conducting shell is placed in a uniform external electric field of magnitude $$

Electrostatic Shielding in a Conducting Sphere

A hollow metallic sphere carries a net charge on its surface, and a point charge is placed inside th

Energy Conversion in Point Charge Interaction

A fixed positive charge $$Q = +2.0 \times 10^{-6} \; C$$ creates an electric field in vacuum. A nega

Evidence of Charge Quantization in Oil-Drop Experiment

An experiment modeled after Millikan's oil-drop experiment produced the following measurements for t

Exploring the Balance of Electric and Gravitational Forces

Design an experiment in which a charged object is suspended in a uniform electric field, balancing t

Invariance of Electric Charge

Electric charge is considered invariant under transformation between inertial frames. This question

Investigating the Role of Dielectric Materials in Capacitors

Design an experiment to measure how the capacitance of a parallel-plate capacitor changes with the i

Motion of a Charged Particle in a Non-Uniform Electric Field

A particle with charge \(q\) and mass \(m\) moves into a region where the electric field varies with

Parallel Plate Capacitor Experiment: Dielectric Misconception

An experiment is designed to measure the capacitance of a parallel-plate capacitor by arranging two

Potential Difference in a Non-Uniform Electric Field

Consider a region where the electric field varies with position according to $$E(x) = 5.0*10^{4} - 2

Proton-Electron Force Comparison

This question examines the forces between a proton and an electron in a hydrogen atom and requires y

RC Circuit Charging

A researcher investigates the charging behavior of a capacitor in an RC circuit. The circuit contain

Series and Parallel Capacitor Network Analysis

A capacitor network is constructed by connecting capacitors in both series and parallel arrangements

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

Verification of the Inverse Square Law for Electric Forces

An experiment measured the electric force between two charged objects as the distance between them w

Work in a Non-Uniform Electric Field

A researcher moves a charge in the non-uniform electric field generated by a fixed point charge. The

Work in a Radial Non-Uniform Electric Field

A positive test charge q is moved radially inward from a distance r₁ to a closer distance r₂ from a

Advanced Transient Analysis in Electric Circuits

A complex circuit contains multiple RC branches with different resistances and capacitances. The tra

Analysis of Variable Resistance in a Circuit

A circuit is set up with a rheostat (variable resistor) controlling the current through a motor powe

Analyzing Capacitors in Series and Parallel

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

Application of Kirchhoff’s Junction and Loop Rules

Consider a circuit where three branches intersect at a junction. Two branches carry currents $$I_1$$

Application of Kirchhoff’s Laws in Complex Circuits

Consider a circuit that has two branches: one branch contains a single resistor and the other branch

Basic Circuit Analysis

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

Battery and Capacitor in Renewable Energy Applications

In a simplified model of a solar panel energy storage system, a battery with an ideal EMF of 18 V an

Battery Internal Resistance and Power Delivery

A battery modeled as an ideal EMF source of 12 V in series with an internal resistance of 2 Ω is con

Battery Internal Resistance and Terminal Voltage

This question investigates the effects of a battery's internal resistance on its terminal voltage wh

Battery Performance and Power Output

A 12 V battery is connected to a resistor, and its terminal voltage, current, and power output are r

Circuit Analysis: Series and Parallel Resistors

In an experiment, a circuit is assembled using a battery with voltage $$V$$ and a network of resisto

Current Flow Analysis in a Simple Battery Circuit

A researcher claims that a circuit composed of a 12 V battery and various resistors produces a conti

Designing a Resistor Network for Specific Equivalent Resistance

You are provided with resistors of values $$5 \Omega$$, $$10 \Omega$$, and $$15 \Omega$$. Design a r

Designing a Voltage Divider Circuit

Design a voltage divider that converts a 24 V supply to a 5 V output using two resistors in series.

Determining Equivalent Capacitance in Series and Parallel

Capacitors can be combined in different ways to achieve a desired equivalent capacitance.

Determining Resistivity of Various Materials

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

Determining the Capacitance Variation Through Geometric Changes

A student explores how the geometry of a parallel-plate capacitor affects its capacitance. The exper

Effect of Dielectric on Capacitance in a Parallel-Plate Capacitor

A parallel-plate capacitor with plate area A and separation d is initially filled with air (dielectr

Effects of Series and Parallel Combinations on Circuit Functionality

An experimental setup features several combinations of resistors and capacitors arranged in both ser

Evaluation of Energy Dissipation in a Resistor

A 10 Ω resistor is connected to a 9 V battery.

Examining Charge Retention in Capacitors: Steady State vs. Transient

A capacitor in a circuit can behave differently depending on whether the battery remains connected o

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 Battery Life: Internal Resistance and Power Loss

A researcher is studying how the increasing internal resistance of a battery affects its performance

Kirchhoff’s Laws: Loop and Junction Analysis

An experiment was conducted on a multi-loop circuit to test Kirchhoff's loop and junction rules. The

Measuring Power Dissipation in Resistive Elements

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

Modeling a Circuit with Mixed Resistors and Capacitors

An experimental study claims that in an RC circuit, a capacitor acts like a short circuit immediatel

Multi-branch Circuit Analysis

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

Multi-loop Circuit Analysis with a Capacitor

A circuit consists of two loops. In the first loop, a resistor of $$4\,\Omega$$ is connected in seri

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 Combination Analysis: Series and Parallel

A report claims that complex resistor networks can be simplified into a single equivalent resistance

Series and Parallel Resistor Analysis

This question examines the behavior of resistors arranged in series and parallel in simple circuits.

Terminal Voltage Variation Under Different Load Conditions

In an experiment, a battery's terminal voltage is measured under varying load resistances. The table

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 Magnetic Field vs. Distance for a Current-Carrying Wire

An experiment measures the magnetic field at various distances from a long, straight current-carryin

Analysis of Magnetic Torque on a Current Loop

A rectangular loop carrying a current $$I = 2.0$$ A is placed in a uniform magnetic field of strengt

Changing Magnetic Flux Through a Circuit

Magnetic flux through a loop can be altered by changes in the loop’s area, the strength of the magne

Circular Motion of a Charged Particle in a Magnetic Field

A charged particle enters a uniform magnetic field perpendicular to its velocity and undergoes unifo

Comparative Analysis of Magnetic Forces on Oppositely Charged Particles

Two particles, one with a positive charge of $$q_1 = +2 \times 10^{-6} \; C$$ and the other with a n

Designing a Magnetic Levitation Experiment

A researcher aims to levitate a small object using a combination of current-carrying coils and perma

Designing an Experiment for Faraday's Law

Faraday’s law states that a changing magnetic flux through a circuit induces an emf. Design an exper

Determination of Solenoid Current through Field Measurements

Students aim to determine the current flowing through a solenoid by measuring the magnetic field ins

Effect of Changing Magnetic Field Strength on Induced Current

A coil is subjected to a magnetic field that decreases linearly from $$B_0$$ to $$B_1$$ over a time

Effects of Varying Angles on Magnetic Force

A negatively charged particle with charge $$q = -3×10^{-6} C$$ is moving at a speed $$v = 1×10^6 m/s

Experimental Determination of Magnetic Permeability

Design an experiment to measure the magnetic permeability of various materials by comparing the magn

Experimental Investigation of Induced EMF in a Varying Magnetic Field

Analyze the induced emf in a coil subjected to a time-varying magnetic field, and discuss the impact

Faraday's Law in a Rotating Loop

A circular loop of radius $$r = 0.03 m$$ is placed in a uniform magnetic field of $$B = 0.2 T$$. The

Induced EMF in a Time-Varying Solenoid Field

A solenoid with 300 turns and a cross-sectional area of 0.05 m² produces an axial magnetic field tha

Investigation of Hysteresis in Ferromagnetic Materials

Design an experiment to investigate the hysteresis behavior in ferromagnetic materials by plotting a

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 Lines Visualization

In this FRQ, you will explore the physical basis and representation of magnetic fields around a bar

Magnetic Force on a U-Shaped Current-Carrying Wire

A U-shaped conducting wire of mass $$m$$ is partially immersed in a uniform magnetic field of magnit

Magnetic Force vs. Current in a Wire

An experiment examines the magnetic force acting on a straight current-carrying wire placed in a uni

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 with Iron Dust

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

Mapping the Magnetic Field of a Current-Carrying Wire

Design an experiment to map the magnetic field produced by a long, straight current-carrying wire an

Measurement of Lorentz Force on a Moving Conductor

A laboratory experiment is set up to measure the Lorentz force acting on a copper bar that slides al

Motional EMF in a Conducting Rod

A conducting rod of length $$l = 0.2$$ m moves at a constant speed $$v = 3.0$$ m/s through a uniform

Motional EMF in a Moving Rod

A conducting rod of length $$L = 0.3 m$$ moves with a constant velocity of $$v = 2 m/s$$ along paral

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

Rotating Coil and Faraday’s Law Experiment

Design an experiment to test Faraday’s Law of electromagnetic induction by using a coil rotating in

Solenoid Magnetic Field Measurement Experiment

A team of students sets out to measure the magnetic field inside a solenoid using a Hall effect sens

Torque on a Current Loop in a Magnetic Field

A rectangular current loop placed in a uniform magnetic field experiences a torque that tends to ali

U-Shaped Wire and Magnetic Force Equilibrium

A U-shaped wire with a mass of $$m = 0.2 kg$$ has a horizontal middle segment of length $$L = 0.4 m$

U-Shaped Wire Current Balance

A researcher studies a U-shaped wire with three segments (two vertical legs and one horizontal segme

Verification of Right-Hand Rule Using Compass Readings

An experiment is conducted where students use a current-carrying wire to generate a magnetic field a

Zero Net Force in U-Shaped Wire Experiment

In a controlled experiment, a U-shaped wire with three segments is partially immersed in a magnetic

Aperture Diffraction Analysis

A rectangular aperture with a width of $$0.5*10^{-3}$$ m and a height of $$1*10^{-3}$$ m is illumina

Chromatic Aberration in Lenses

Chromatic aberration occurs when a lens fails to focus all wavelengths to the same point. Answer the

Converging Lens: Image Magnification and Power Calculation

This question deals with image formation through a converging lens, requiring you to determine the f

Diverging Lens and Virtual Image Formation

Diverging lenses produce virtual, diminished, and upright images. Analyze the image formation by a d

Effects of Wavelength Change in Interference Patterns

This question examines the effect of changing the wavelength of light on the interference patterns p

Electromagnetic Wave Interference and Phase Difference

A diagram is provided showing two coherent electromagnetic waves with a phase difference interfering

Electromagnetic Wave Propagation in Different Media

An experiment measured the speed of light in various media. The table below presents the recorded sp

Experimental Interference Pattern Analysis

This question requires you to analyze experimental data from an interference experiment and evaluate

Fiber Optics and Total Internal Reflection

An optical fiber operates on the principle of total internal reflection. The core of the fiber has a

Image Formation in Plane Mirrors

Consider a scenario where a person stands in front of a plane mirror at a distance $$d$$ from the mi

Image Formation with a Concave Mirror

A student investigates image formation using a concave mirror. In the experiment, a concave mirror w

Impact of Wavelength on Single Slit Diffraction Patterns

In an experiment, a student investigates how changing the light's wavelength affects the diffraction

Interference in Thin Films

A researcher studies the colorful interference patterns observed in a thin soap film, where film thi

Investigation of Diffraction Gratings in Spectroscopy

Diffraction gratings are key components in spectroscopy, providing high resolution in wavelength sep

Lens Power Calculations and Image Magnification

In a converging lens experiment, an object placed 10 cm from the lens produces a real image that is

Lens Power Determination Based on Image Size

This question requires you to determine the power of a converging lens based on the magnification ob

Light Refraction through Multiple Media Interfaces

Light may pass through several media in succession, undergoing refraction at each interface. Analyze

Optical Fiber Signal Loss Analysis

An optical fiber experiences a signal loss of 0.2 dB per meter. (a) Express the transmitted intens

Polarization and Wave Interference

Light that is initially unpolarized is passed through a series of polarizing filters. Answer the fol

Polarization through Multiple Polarizers

A beam of light with an initial intensity \(I_0\) is passed through a series of polarizers. In the f

Reflection and Refraction with Wavelength Effects

A beam of light travels from air ($$n_1 = 1.0$$) into a glass medium ($$n_2 = 1.5$$) at an incident

Reflection and Refraction: Application of Snell’s Law

This question examines the application of Snell's law to a light beam incident on a glass surface an

Reflection and Refraction: Investigating Angle Relationships at a Glass Interface

Design an experiment to study both reflection and refraction of light at a glass-air interface. Your

Single Slit Diffraction Analysis

In a single slit experiment, a diffraction pattern is recorded. A graph of intensity versus angle is

Spherical Mirrors: Concave Mirror Ray Tracing

An experiment is performed using a concave mirror. The following table shows measurements for two di

Thin Converging Lens Imaging

A bi-convex (converging) lens with a focal length of 10 cm is used to form an image of an object tha

Thin Lenses: Converging Lens Analysis

An object is placed 10 cm from a converging lens, forming a real image that is twice the height of t

Total Internal Reflection Analysis

A light beam travels in water (index of refraction $$n=1.33$$) and approaches the water-air boundary

Total Internal Reflection and Critical Angle Determination

This question focuses on deriving the condition for total internal reflection and applying it to det

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

Gamma Decay and Energy Emission

A researcher analyzes gamma decay in an excited nucleus. Answer the following:

Investigating Electronic Transition Spectra

A researcher examines the emission spectrum generated by electrons in a hydrogen-like atom with ener

Nuclear Fusion Reaction Analysis

A researcher studies the fusion reaction between deuterium nuclei represented by: $$^2H + ^2H \right

Photodisintegration of a Deuteron

A study is conducted on the photodisintegration of deuterium. Given that the binding energy of a deu

Photoelectric Effect on Aluminum

A researcher studies the photoelectric effect on an aluminum surface by illuminating it with light o