AP Physics 2: Algebra-Based FRQ Room

Airflow and Lift on an Aircraft Wing using Bernoulli's Principle

An aircraft wing is designed so that the airspeed over the top surface is 250 m/s and beneath the wi

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 Airfoil

An experimental report claims that the difference in airspeed over the top and bottom surfaces of an

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

Airflow over an Airfoil Experiment

A wind tunnel experiment investigates the pressure distribution on an airfoil. Sensors along the cho

Analysis of Experimental Data: Fluid Pressure on Vertical Surfaces

A civil engineer conducts an experiment to measure the pressure exerted by water on a vertical surfa

Bernoulli's Equation and Pressure Variation in a Constricted Pipe

A pump forces water (with density $$1000\;kg/m^{3}$$) through a pipe that gradually narrows. At poin

Bernoulli’s Principle and Pressure Measurements

Water is pumped through a horizontal pipe that constricts and expands in diameter. At Point 1 in the

Bernoulli's Principle Experimental Design

A researcher plans to design an experiment to assess how changes in the pipe's cross-sectional area

Bernoulli's Principle in a Constricted Pipe

A pump forces water through a horizontal pipe that narrows gradually. At point 1 the cross-sectional

Buoyancy and Archimedes’ Principle Experiment

An object with a mass of $$150\,kg$$ and a volume of $$0.75\,m^3$$ floats in a fluid of unknown dens

Buoyancy and Floatation Analysis

A wooden block used in an experiment has a mass of 150 kg and a volume of 0.75 m³. It is placed in a

Buoyancy and Floating Objects Analysis

An object with a mass of 150 kg and a volume of 0.75 m³ is floating in a fluid. In one case, the flu

Buoyancy in a Variable-Density Atmosphere: Weather Balloon Analysis

A weather balloon is launched at ground level, where the atmospheric density is $$1.225\,kg/m^3$$. A

Buoyancy in Marine Vessel Design

A researcher studies how buoyancy principles are applied to ensure that marine vessels float.

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

Column Pressure Analysis

A series of experiments is conducted to analyze the pressure exerted by vertical cement columns on t

Computer Simulation of Fluid Flow in Pipes

A researcher uses a computer simulation to model fluid flow in pipes containing obstacles. The simul

Continuity Equation in a Constricted Pipe

A horizontal pipe carries water (density $$1000\;kg/m^3$$) at a flow speed of $$6\;m/s$$. At one sec

Density Determination via Fluid Displacement

Design an experiment to measure the density of an irregularly shaped object using the method of flui

Density Variation in Immiscible Fluids

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

Depth-Dependent Pressure Analysis

A cylindrical tank is filled with oil having a density of $$800\;kg/m^3$$. The oil column has a heig

Designing a Wind Tunnel Experiment to Validate Bernoulli's Effect

A researcher is tasked with designing a wind tunnel experiment to validate Bernoulli’s effect on a s

Designing an Experiment on Fluid Flow Through Pipes

This question requires designing an experiment to investigate the effect of pipe diameter on fluid f

Determining Object Volume through Fluid Displacement

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

Developing an Experiment for Continuity Equation Verification

Design a controlled experiment to verify the continuity equation using water (density $$1000\;kg/m^3

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

Dynamic Pressure in a Wind Tunnel

In a wind tunnel experiment, air flows at a speed of $$15\,m/s$$. Given that the density of air is $

Energy Conversion in Hydraulic Systems

Hydraulic systems utilize fluid flow to convert energy and perform work. As fluid flows, energy is t

Energy Loss and Friction in Extended Pipe Flow

Water is pumped through a long, straight pipe, and energy losses occur due to friction along the pip

Experimental Analysis of Flow Speed Using Continuity Equation

In an experiment, water flows through a horizontal pipeline with varying cross-sectional areas. The

Flow Speed Adjustments Due to Pipe Diameter Variations

A water pipeline experiences variations in diameter. The following table lists measurements for two

Flow through Varying Pipe Diameters

Water flows through a horizontal pipe that narrows. At Section 1, the pipe has a radius of 2 cm and

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.

Graphical Analysis of Flow Speed Variation

A researcher has collected experimental data on the relationship between a pipe's cross-sectional ar

Hydrostatic Pressure in a Liquid Column

Consider an open tank filled with a liquid of density $$\rho$$. The hydrostatic pressure at a depth

Investigating Siphon Dynamics and Flow Maintenance

Design an experiment to study the operation of a siphon system, focusing on the conditions necessary

Lift Generation in Airfoils

An airplane wing is designed so that air flows over its upper surface at a higher speed than beneath

Mapping Fluid Pressure Distribution Using Sensors

Design an experiment to map the pressure distribution within a fluid container by using multiple pre

Measuring Buoyant Force with a Submerged Object

A student conducts an experiment to measure the buoyant force acting on an object of volume $$0.2 \c

Modeling Fluid Flow in a Conical Pipe

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

Non-uniform Flow Through Constricted Channel Error

A student constructs an apparatus to measure fluid velocity in a channel that narrows and changes sh

Pitot Tube Velocity Measurement

A Pitot tube is used to determine the velocity of air. The difference between the stagnation pressur

Pressure Distribution in an Accelerating Container

A rectangular container filled with water (density $$1000\;kg/m^3$$) is accelerated horizontally at

Pressure Variations in a Natural Lake

This question connects fluid mechanics with environmental applications by calculating hydrostatic pr

Pump Power in a Multi-Elevation Piping System

A pump moves water (density = 1000 kg/m³) through a piping system where the water is elevated by 2 m

Real-World Application: Fluid Flow in a Piping System

A municipality is evaluating a new water piping system designed to transport water from a reservoir

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

Static Fluid Pressure in a Tank

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

Structural Column Pressure

This question examines the calculation of pressure exerted by a vertical structure and how variation

Surface Pressure Analysis of a Column

A vertical column of cement has a base area of $$0.5\,m^2$$, a height of $$2\,m$$, and a density of

Temperature Effects on Fluid Viscosity and Flow

In an experiment, the flow rate of a viscous fluid through a fixed nozzle is measured at various tem

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

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

Analysis of Heat Conduction Through Materials

A flat slab of material has a thickness of 0.05 m and an area of 1.0 m². The temperature difference

Application of the First Law of Thermodynamics

A gas within a piston undergoes a quasi-static process in which 500 J of heat is added to the system

Clausius-Clapeyron Equation and Phase Transitions

The Clausius-Clapeyron equation relates vapor pressure to temperature during phase transitions. (a)

Comparative Analysis of Convection and Radiation Heating

A scientist conducts an experiment comparing two heating methods: convection and radiation. The tabl

Convection Versus Conduction in Fluid Heating

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

Conversion between Energy and Work in Cyclic Processes

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

Designing a Heat Engine for Maximum Efficiency

A researcher is designing an idealized Carnot heat engine operating between a high-temperature reser

Effect of Temperature on rms Velocity

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

Energy Conversion in a Steam Engine

A steam engine operates with an efficiency of 30% and absorbs 2000 J of heat per cycle. (a) Calcula

Entropy Changes in Thermodynamic Processes

A system undergoes an irreversible expansion followed by a reversible compression. Analyze and evalu

Entropy vs. Temperature Measurement Experiment Error

A student aims to study the change in entropy of a material as it is gradually heated. A thermocoupl

Error Analysis in Thermodynamics Measurements

A laboratory experiment measuring the temperature and pressure of a gas in a sealed container shows

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.

Exploring Kinetic Molecular Theory via Maxwell-Boltzmann Distribution

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

Force Exerted by Gas in a Cylindrical Container

A cylindrical container with a radius of 15 cm and height of 30 cm contains 0.6 moles of an ideal ga

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

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

Heat Engine Work Cycle Analysis

A heat engine operates by drawing $$Q_H = 800\,J$$ of heat from a high-temperature source and discar

Ideal Gas Pressure Analysis

A cylindrical container with a closed lid has a radius of $$0.15\;m$$ and a height of $$0.30\;m$$. I

Investigating Thermodynamic Processes: Isobaric vs Isochoric

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

Kinetic Energy and Molecular Speeds

The average kinetic energy of gas molecules is given by $$K_{avg} = \frac{3}{2} k_B T$$. (a) Derive

Maxwell-Boltzmann Distribution Analysis

The Maxwell-Boltzmann distribution characterizes the spread of molecular speeds in an ideal gas. (a)

Radiative Heat Transfer Trend Analysis

An experiment measures the rate of radiative heat transfer from a heated object as a function of the

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

Temperature Change and Molecular Speed Distribution

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

Thermodynamic Efficiency and Real Engines

Real heat engines are subject to various losses and cannot achieve the ideal efficiencies predicted

Thermodynamics and Mechanical Work in an Automobile Engine

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

Understanding Temperature Scales in Thermodynamic Calculations

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

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

Verification of RMS Speed Dependence on Temperature

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

Work in Cyclic Thermodynamic Processes

A researcher analyzes two different cyclic processes shown on P–V diagrams. Process 1 follows a rect

Work in Isobaric and Isochoric Processes Analysis

A gas in a cylinder undergoes two separate experiments. In Experiment 1 (isobaric), the gas expands

Analysis of an Electric Dipole Field

An electric dipole consists of two charges, \(+q\) and \(-q\), separated by a distance \(d\). (a) D

Analysis of Electric Dipole Field Measurements

An experimental setup measures the electric field magnitude at various distances along the perpendic

Capacitor: Potential Difference and Energy Storage

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

Charge Redistribution via Induction

Two identical, initially neutral conducting spheres are placed in contact on an insulating stand. A

Charging an RC Circuit

Consider an RC circuit connected to a 12 V battery. The circuit consists of a resistor with resistan

Charging Methods Comparison

A researcher conducts two experiments to charge a neutral metal sphere. In Experiment 1, the sphere

Comparative Analysis of Charging Methods

In a laboratory setting, two objects made from different materials—one metal (a good conductor) and

Comparative Analysis: Charging by Conduction vs. Induction

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

Coulomb Force Analysis in a Two-Charge System

An experiment investigates the electric force between two fixed charged spheres as a function of the

Coulomb's Law and Electric Field Vector Addition in an Equilateral Triangle

Three point charges are placed at the vertices of an equilateral triangle with a side length of $$0.

Dielectric Effects in a Capacitor

A parallel-plate capacitor with a plate separation of 1.0 mm is initially filled with air (dielectri

Dielectric Effects on Capacitance Experiment

In a parallel-plate capacitor experiment, the capacitance is measured with and without the insertion

Dipole Electric Field Analysis

This question examines the calculation and analysis of the electric field created by an electric dip

Distance Dependence in Coulomb's Law

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

Effect of Temperature on Dielectric Constant in Capacitors

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

Electric Field and Potential of an Infinite Charged Sheet

A very large sheet has a uniform surface charge density σ = 5.0×10^-6 C/m². Answer the following: (a

Electric Field Lines and Equipotential Mapping Misinterpretation

In a laboratory experiment, a student is tasked with mapping electric field lines and equipotential

Electric Field Lines at Media Boundaries

This problem examines how electric field lines behave at the boundary between two different media an

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 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 Energy Conversion in a Charged Projectile Experiment

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

Electric Potential Energy Conversion in a Point Charge Field

A positive charge is released from rest at a distance of 10 cm from a fixed positive charge and is l

Electric Potential from Multiple Point Charges

Two fixed point charges are placed along the x-axis: $$q_1 = +3.0 \times 10^{-6}\,C$$ at $$x = 0\,m$

Equipotential Surfaces and Electric Field Lines

For an isolated positive point charge: Part A: Describe the geometry of its equipotential surfaces.

Forces in the Hydrogen Atom

Consider a hydrogen atom in which a proton (mass = 1.6×10⁻²⁷ kg, charge +e) and an electron (mass =

Graphical Analysis of Electric Field Variation with Distance

Experimental measurements were made of the electric field strength at varying distances from a charg

Influence of Plate Area on Capacitor Capacitance

Design an experiment to determine how changing the area of the plates of a parallel-plate capacitor

Investigating Coulomb's Law in a Controlled Experiment

Design an experiment to measure the electric force between two charged spheres as a function of sepa

Linear Variation of Electric Potential near a Charged Sheet

An experiment measured the electric potential at several distances from an infinite charged sheet. A

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

Measuring Electric Field Intensity from a Conductive Plate

Design an experiment to measure the electric field intensity at various distances along the axis per

Measuring Electric Potential Variations from a Point Charge

Develop an experimental design to measure the electric potential at various distances from a fixed p

Net Force on a Central Charge in a Square Configuration

Four equal positive point charges are placed at the vertices of a square with side length 10 cm, and

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

RC Circuit: Charging a Capacitor

A capacitor with a capacitance of $$100\,\mu F$$ is connected in series with a resistor of $$10\,k\O

Superposition of Forces in a Square Charge Configuration

Consider four equal positive point charges placed at the vertices of a square with each side measuri

Verification of Charge Quantization

A researcher performs an oil drop experiment to verify the quantization of electric charge. The meas

Work Done in a Uniform Electric Field

A positive charge $$q$$ is moved from one equipotential surface to another within a region that has

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

Analysis of Ammeter and Voltmeter Placement

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

Analysis of Non-Ohmic Behavior in Materials

Some materials do not obey Ohm’s Law under certain conditions, exhibiting non-ohmic behavior. Answer

Analyzing Power Dissipation in a Resistor Network

Consider a resistor network connected to a $$12~V$$ battery.

Analyzing the Effect of Wire Geometry on Resistance Measurements

A student investigates how the resistance of a wire depends on its length and cross-sectional area b

Analyzing Thermal Effects on Resistivity in Conductor Materials

A student measures the resistance of a copper wire at various temperatures to study the temperature

Analyzing Transients in RC Circuits with Switching

Consider a circuit where a capacitor, initially uncharged, is connected in series with a resistor an

Capacitor Charging in an RC Circuit

In an RC circuit, a capacitor is charged by connecting it to a battery through a resistor. Consider

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 *

Comparative Analysis of Capacitor Charging Profiles

Two RC circuits are set up using identical resistor and capacitor values: $$R = 3 \Omega$$ and $$C =

Comparative Energy Storage: Batteries vs Supercapacitors

Different technologies store energy in distinct ways. Batteries use chemical reactions, whereas supe

Comparing Conductor Materials: Effect on Efficiency

Different materials have different resistivities, which affect their performance in circuits. Consid

Comprehensive Circuit Design and Analysis

You are designing a circuit board that includes a resistor network and a smoothing capacitor. The ci

Critically Evaluating the Role of Wire Material in Circuit Performance

A claim has been made that using wires made of materials with low resistivity, such as copper, enhan

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 Circuit for LED Brightness Control

An electronics designer wants to control the brightness of an LED using a variable resistor (rheosta

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 an RC Circuit for a Target Time Constant

Design an RC circuit that achieves a time constant of $$0.5\,s$$. You are provided with capacitors r

Determining Resistivity from Measured Data

A student measures several parameters of a wire in order to calculate its resistivity.

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 Resistor Arrangement on Circuit Current Distribution

A circuit consists of a 12 V battery connected to a resistor network featuring both series and paral

Effects of a Variable Resistor on Circuit Behavior

A variable resistor is used in a series circuit powered by a 15V battery.

Equivalent Capacitance for Series and Parallel Configurations

Two capacitors, one of $$4 \text{ F}$$ and the other of $$6 \text{ F}$$, are arranged in different c

Equivalent Resistance in Complex Resistor Networks

A circuit consists of five resistors arranged as follows: Resistors $$R_1$$ and $$R_2$$ (each $$10\,

Evaluating a Modified Ammeter Design for Improved Accuracy in Low-Current Measurements

A claim has been made that a newly designed ammeter with ultra-low internal resistance provides sign

Experiment to Determine Battery Internal Resistance

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

Investigative Lab on Short-Circuiting Capacitors and Resistors

A misconfigured circuit experiment resulted in a capacitor being inadvertently short-circuited by co

Kirchhoff's Laws in a Multi-Loop Circuit

A circuit consists of two loops sharing a common resistor. In Loop 1, a 12 V battery is connected in

Measurement and Analysis of Conductivity in Different Materials

The electrical properties of materials can be compared by considering their conductivity (the invers

Modeling the Behavior of a Heated Resistor in an Electrical Circuit

A resistor with an initial resistance of 100 Ω at 20°C has a temperature coefficient of 0.004/°C. If

Modifying Resistor Values for Current Limiting in LED Circuits

An LED with a voltage drop of 2 V requires a current of 20 mA for optimal performance. It is powered

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

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 Analysis

A laboratory experiment is conducted to measure the electrical characteristics of resistors. The fol

Power Dissipation Optimization in Resistor Networks

A laboratory experiment compares power dissipation in two resistor network configurations: one with

Series-Parallel Circuit with Capacitors and Resistors

A complex circuit is built with both resistor and capacitor networks. In the resistor network, resis

Transient Analysis in an RC Circuit

A circuit with a resistor of $$200\,\Omega$$ and a capacitor of $$50\,\mu F$$ is connected to a $$12

Transient Behavior in RC Circuit: Initial vs Steady-State

An RC circuit is constructed with a $$12~V$$ battery, and two branches: one branch contains a $$6~\O

Transient Response Analysis in an RC Circuit

An RC circuit is connected to a $$10 \text{ V}$$ battery with a resistor of $$5 \Omega$$ and a capac

Transient Response in an RC Circuit with Multiple Resistors

Design and analyze a more complex RC circuit that includes multiple resistors in series and parallel

Wire Resistance Calculation

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

Calculating the Magnetic Field Around a Current-Carrying Wire

A long, straight wire carrying a steady current produces a magnetic field in the space around it. Us

Charged Particle Force Analysis

A proton with charge $$q = +1.6×10^{-19} C$$ enters a uniform magnetic field $$B = 0.3 T$$ with a sp

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

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

Critical Angle for Maximal Magnetic Force

A researcher investigates the dependence of the magnetic force on a charged particle with the equati

Design of a Magnetic Braking System

Design a magnetic braking system for a roller coaster that uses the principles of electromagnetic in

Designing an Electromagnet with a Solenoid

Electromagnets can be constructed using solenoids. In this problem, you will derive the magnetic fie

Designing an Electromagnetic Induction Experiment

This FRQ requires designing an experiment to investigate how the speed of a sliding rod affects the

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

Determining Magnetic Field Direction Around a Wire

A long, straight vertical wire carries a current of 15 A upward. Around the wire, four points (A, B,

Electromagnetic Induction in a Rotating Loop

A circular loop rotates in a uniform magnetic field, causing a time-varying magnetic flux and induce

Energy Conversion in an Electromagnetic Generator

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

Evaluating the Magnetic Field of a Current-Carrying Wire

An experiment is conducted to measure the magnetic field strength around a long, straight current-ca

Exploring Motional EMF in a Moving Conductor

Design an experiment to measure the motional emf generated when a conductor moves through a uniform

Faraday’s Law and Rotating Loop

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

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

Faraday's Law in Rotating Loop Experiment

An experiment is conducted in which a circular loop rotates at a constant angular speed in a uniform

Force Cancellation in a U-Shaped Conductor

Design an experiment to investigate the conditions under which the net magnetic force on a U-shaped

Force on a Charged Particle in a Non-Uniform Magnetic Field

A charged particle with charge $$q$$ moves with constant speed $$v$$ in a region where the magnetic

Force on a Proton Near a Current-Carrying Wire

A proton moves near a long, straight wire that carries a constant current. Analyze the magnetic fiel

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 Rectangular Loop Under Rotation

A rectangular loop of wire measuring 0.1 m by 0.2 m is placed in a uniform magnetic field of 0.5 T.

Induced EMF in a Rotating Rod

A conducting rod of length $$L = 0.4 m$$ rotates about one end in a uniform magnetic field $$B = 0.3

Interaction Between Bar Magnets

Two bar magnets are placed facing each other with like poles (both North) at a separation of $$d = 0

Investigating Temperature Effects on Superconducting Magnetic Fields

Superconductors exhibit unique magnetic properties, such as the Meissner effect, when cooled below a

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

Magnetic Field Mapping with Iron Filings

A permanent magnet’s surrounding region is investigated using iron filings. Explain how iron filings

Magnetic Flux and Loop Angle

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

Magnetic Flux Change in a Sliding Rod Circuit

A rectangular circuit has one side that is a conducting rod sliding in a uniform magnetic field. Ana

Mapping Magnetic Field Lines using Iron Dust

In an experiment, a bar magnet is placed on a sheet and iron dust is sprinkled over it to visualize

Mapping Magnetic Field Strength vs. Distance

Design an experiment to map how the magnetic field strength decreases with distance from a magnet. Y

Mapping Magnetic Field Using Compasses

You are provided with a long, straight current-carrying wire and several small compass needles. Your

Mapping Magnetic Fields around a Bar Magnet

A researcher is studying the magnetic field of a standard bar magnet in a controlled laboratory sett

Measurement of Magnetic Field Gradient near an Electromagnet

A research team uses a magnetic field probe to measure the gradient of the magnetic field in the vic

Motion of a Charge in Perpendicular Electric and Magnetic Fields

A charged particle with charge $$q$$ and mass $$m$$ enters a region where there is a uniform magneti

Motional EMF and Energy Conversion Analysis

A conducting rod of length $$l = 0.8 \; m$$ moves to the right at a constant speed of $$v = 4 \; m/s

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 Conductor

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

Motional EMF in Non-Uniform Magnetic Fields

Moving conductors in non-uniform magnetic fields can develop complex distributions of induced emf. A

Right-Hand Rule Applications in Magnetic Force Directions

Using the right-hand rule, determine the direction of the force on charged particles moving in a mag

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

Solenoid Magnetic Field

This FRQ explores the magnetic field inside a solenoid through derivations, calculations, and concep

Trajectory Analysis of a Charged Particle in a Non-Uniform Magnetic Field

A charged particle with charge $$q$$ and mass $$m$$ enters a region where the magnetic field varies

Trajectory of a Proton Near a Current-Carrying Wire

A proton moving at a speed of $$2 \times 10^5 \;m/s$$ passes at a distance of 4 cm from a long, stra

U-Shaped Wire in a Magnetic Field

A U-shaped wire is immersed in a uniform magnetic field. Analyze the forces on its different segment

Uniform Magnetic Field in a Solenoid Experiment

An experiment is conducted using a solenoid as an electromagnet, and it is claimed that the magnetic

Uniform Magnetic Field Inside a Solenoid

A solenoid is constructed with 400 turns and has a length of 0.25 m. It carries a current of 2 A. An

Zero Net Force Condition in a U-Shaped Conductor

A U-shaped conductor is placed in a uniform magnetic field and carries a current. Under specific con

Combined Lens System Analysis

A two-lens system consists of a converging lens with focal length $$f_1 = 30 \text{ cm}$$ and a dive

Converging Thin Lens Image Formation

A researcher sets up a converging lens with a focal length of $$15$$ cm to project an image. An obje

Critical Angle Determination for Various Media

A researcher is studying critical angles when light passes from glass (with $$n=1.5$$) into differen

Diffraction Grating Analysis

A researcher uses a diffraction grating with 5000 lines per centimeter to analyze the spectrum of a

Diffraction Grating Wavelength Measurement

A student uses a diffraction grating with 5000 lines per centimeter to measure the wavelength of an

Diffraction Gratings Analysis

A diffraction grating with 5000 lines per centimeter is used to analyze sodium light with wavelength

Diverging Lens and Virtual Image Formation

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

Diverging Lens: Image Formation Analysis

This question involves analyzing image formation by a diverging lens using the thin lens equation an

Electromagnetic Spectrum Frequency Analysis

Electromagnetic radiation spans a wide range of wavelengths and frequencies. This question explores

Electromagnetic Spectrum Identification and Frequency Calculation

The electromagnetic spectrum covers a wide range of wavelengths and frequencies. Refer to the table

Electromagnetic Wave Characteristics and Frequency Calculation

Using the table provided, analyze the relationship between wavelength and frequency of electromagnet

Electromagnetic Wave Propagation Analysis

Electromagnetic waves consist of oscillating electric and magnetic fields and travel through a vacuu

Experimental Design: Evaluating Light Behavior in Combined Mirror-Lens Systems

An optical system combines a concave mirror and a converging lens to form an image. The following ta

Frequency Determination of Green Light: Speed of Light Misassumption

A student attempts to calculate the frequency of green light by measuring its wavelength with a spec

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 from Coherent Light Sources

Two coherent, monochromatic light sources produce an interference pattern on a distant screen. Answe

Interference from Multiple Sources

Three coherent light sources, each emitting light of wavelength $$\lambda = 650 * 10^{-9}$$ m, are a

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

Multi-Wavelength Interference Experiment

In an experiment using a diffraction grating, two monochromatic light sources are employed: red ligh

Optical Data Analysis from Spherical Mirror Measurements

An experiment is conducted where an object is placed at various distances from a concave mirror, and

Photon Energy Calculation in the Electromagnetic Spectrum

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

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: 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

A single slit of width $$a = 0.1\,mm$$ is illuminated by monochromatic light with a wavelength of $$

Spherical Mirror Ray Tracing and Image Analysis

A student investigates the formation of images using a concave mirror through ray tracing. The exper

Spherical Mirrors: Concave Mirror Ray Tracing

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

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 Lenses: Converging Lens Analysis

In an experiment involving a converging lens, measurements were taken for various object distances.

Bohr Model and Atomic Spectra

A researcher is investigating the emission spectrum of a hydrogen-like ion. The energy levels in thi

Investigating Electronic Transition Spectra

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

Nuclear Composition and Isotope Identification

A researcher is examining a nuclide represented by $$^{63}_{29}X$$. Using this information, address

Nuclear Fusion Reaction Analysis

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