AP Physics 2: Algebra-Based FRQ Room

Accelerated Fluid in an Elevator Experiment

A sealed container filled with water (density = $$1000 \; kg/m^3$$) is placed inside an elevator tha

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 Airplane Wing via Bernoulli's Equation

Airflow over an airplane wing results in a pressure difference that contributes to lift. Answer the

Airfoil Pressure Distribution Study

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

Analyzing Fluid Flow in a River System

A river exhibits variations in cross-sectional area and flow speed along its course. Measurements at

Application of Bernoulli's Equation in a Constricting Pipe

A pump forces water through a pipe that gradually narrows. At Point 1 (the wider section), the cross

Ballast Systems in Submarines: Buoyancy Control

A submarine uses ballast tanks to adjust its buoyancy. Consider a submarine with an overall volume o

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 Principle and Aircraft Lift

Air flows over the upper and lower surfaces of an airplane wing. In a certain section along the wing

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 Flow System

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

Bernoulli's Principle in a Constricted Pipe

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

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 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 Objects

An object with a mass of 150 kg and a volume of 0.75 m³ is placed in a fluid with a density of 800 k

Buoyancy and Stability of a Floating Body

A rectangular boat with a flat bottom is floating in freshwater (density = 1000 kg/m³). The boat has

Buoyant Stability and Metacentric Height in Floating Bodies

A floating vessel is designed with specific dimensions to ensure stability. A diagram of the vessel’

Channel Flow Dynamics Analysis

A researcher examines fluid flow in a channel with varying cross-sectional areas, applying the conti

Characterizing Fluid Flow with Reynolds Number

A research group claims that in a pipe with a diameter of 0.1 m, water flowing at 1 m/s has a Reynol

Column Pressure Analysis

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

Column Pressure Experiment

A researcher investigates the pressure exerted on the ground by a vertical concrete column. The colu

Continuity Equation and Flow Rate

Water flows through a circular pipe. At Section 1, the pipe has a radius of $$2\,cm$$ and the water

Continuity Equation and Flow Rate in a Non-Uniform Pipe

Water flows through a pipe whose cross-sectional area changes along its length. At point 1 the pipe

Density and Hydrostatic Pressure in a Liquid Column

A lab technician is given a sealed container holding $$1 \times 10^{-3} \; m^3$$ of oil with a mass

Density Determination Experiment

A researcher is investigating the density of three different fluids in the lab. The aim is to accura

Designing a Pipeline: Balancing Pressure and Flow Rate

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

Designing an Optimal Fluid Transport System

In a chemical plant, an optimal fluid transport system needs to be designed for a viscous liquid. De

Determining Buoyant Force on a Partially Submerged Object

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

Dynamic Pressure and Airspeed from Pitot Tube Measurements

A Pitot tube is used on an aircraft to measure dynamic pressure, which is then used to calculate the

Effect of Temperature on Fluid Density and Pressure

A container holds a fluid that is heated from 20°C to 80°C, causing its density to decrease from 100

Effect of Temperature on Fluid Properties

This problem investigates how temperature changes affect fluid properties such as density and viscos

Examining Temperature Effects on Density and Pressure

A fluid contained in a sealed vessel is heated from $$20^\circ C$$ to $$80^\circ C$$. At $$20^\circ

Flow Rate Experiment with Variable Pipe Diameters

A mechanical engineer conducts an experiment in a pipe where the diameter changes in three sequentia

Flow Rate in a Constricted Pipe

Consider a circular pipe carrying water. The pipe has a radius of 2 cm and the water flows at a spee

Flow Rate in a Constricted Pipe Using the Continuity Equation

Water flows through a horizontal pipe that changes diameter. At Section 1 the pipe has a radius of 3

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

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 Statics in Two-Layer Immiscible Liquids

A container holds two immiscible liquids. The top liquid (Liquid A) has a density of $$900 \cdot kg/

Graphical Analysis of Flow Continuity

This problem uses a provided graph to analyze the relationship between flow speed and pipe cross-sec

Graphical Analysis of Flow Speed Variation

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

Hydrostatic Pressure Analysis

A researcher investigates hydrostatic pressure in a fluid system. In an experiment conducted with wa

Hydrostatic Pressure in a Tank

This problem analyzes hydrostatic pressure in a fluid and the effect of atmospheric pressure on tota

Influence of Viscosity on Flow Rate: Exploring Deviations from the Ideal Model

In an experiment, the predicted volume flow rate through a pipe using the continuity equation differ

Modeling Fluid Flow in a Conical Pipe

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

Oil-Water Separation in Multi-Phase Fluid Systems

An experiment is conducted in a container to investigate oil-water separation based on density diffe

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 Continuity

An experiment examines fluid flow through a pipe with a constricted section. The following table sho

Pressure on Submerged Structures: Dam Windows

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

Real-Time Fluid Pressure Monitoring

In a dynamic fluid system, pressure can vary rapidly with transient changes such as sudden valve clo

Siphon Action Analysis

A siphon is used to transfer water from a container. The highest point of the siphon tube is 2 m abo

Solid Column Pressure Calculation

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

Submerged Volume Determination Error in Buoyancy Experiment

A student designs an experiment to determine what fraction of an object's volume is submerged when i

Tank Discharge Flow Experiment

An experiment investigates the discharge of water from a tank through a small orifice at the bottom.

Temperature Effects on Fluid Density and Pressure

A particular fluid has a density of 950 kg/m³ at 20°C and its density decreases by 0.2% for every 1°

Testing Bernoulli's Principle in a Venturi Tube

A researcher is using a Venturi tube to study fluid velocities in water (density = $$1000\;kg/m^{3}$

The Impact of Temperature on Fluid Viscosity and Flow

During an experiment, it was observed that the viscosity of a fluid decreases as temperature increas

Turbulent vs. Laminar Flow in a Conduit

A fluid flows through a horizontal pipe, and its flow regime (laminar or turbulent) depends on the R

Adiabatic Expansion and Temperature Change

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

Analyzing Deviations from the Ideal Gas Law

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

Analyzing Gas Mixtures with Dalton's Law

In a container, two different ideal gases are mixed together. Dalton's Law of Partial Pressures stat

Comparing Isothermal and Adiabatic Processes in a P-V Diagram Experiment

An experiment uses a P-V diagram to compare isothermal and adiabatic processes. Two distinct paths a

Designing a Convection Experiment

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

Designing a Thermos: Minimizing Heat Transfer

A thermos is designed to keep liquids hot by minimizing heat transfer. Discuss the design features c

Determining Molecular Mass of a Gas via Ideal Gas Law Measurements: Experimental Design

The molecular mass of a gas can be determined by measuring its pressure, volume, temperature, and th

Effect of Temperature on Molecular Speed

A researcher investigates how the root-mean-square (rms) velocity of gas molecules depends on temper

Effect of Temperature on RMS Velocity

Given that $$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$ for an ideal gas, (a) Explain the functional depend

Effects of Volume Changes on Gas Pressure and Work in Isobaric Processes

In an isobaric process, a gas expands or contracts at constant pressure, doing work on or by the sur

Energy Conservation in a Closed System

A sealed container undergoes a process during which 500 J of heat is added and 200 J of work is perf

Entropy and the Second Law

Consider a process where 200 J of heat is transferred from a reservoir at 500 K to a reservoir at 30

Entropy and the Second Law

The Second Law of Thermodynamics introduces the concept of entropy, which is often associated with t

Entropy Change Measurement in a Spontaneous Process: Experimental Design

Entropy is a measure of disorder and increases in spontaneous processes. Design an experiment to mea

Experimental Verification of the Zeroth Law of Thermodynamics

An experiment is devised to verify the Zeroth Law of Thermodynamics using three objects. Object C is

First Law of Thermodynamics in a Closed System

An experiment on a closed system records the changes in internal energy, heat added, and work done o

Heat Engine Work Cycle Analysis

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

Heat Engines and Maximum Efficiency

No heat engine can achieve 100% efficiency due to inherent energy losses. (a) Explain why complete c

Heat Transfer Conduction/Convection Experiment Error

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

Impact of Temperature Variations on Gas Density

An experiment investigates how the density of a gas in a container changes as the temperature is inc

Investigating Specific Heat and Energy Transfer in Gases

The specific heat capacity at constant volume, \(C_V\), is a measure of the energy required to raise

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 vs. Adiabatic Processes

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

Kinetic Energy and Temperature Relationship

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

Modes of Heat Transfer: Conduction, Convection, and Radiation

A copper rod of length $$L$$ and cross-sectional area $$A$$ experiences a temperature difference $$\

Pressure Changes in an Isochoric Process

In an isochoric process, a gas is heated while its volume remains constant, causing the pressure to

Pressure Force in a Confined Gas

A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of an ideal gas at 433 K.

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

Real Gas Behavior at High Pressures

At high pressures, real gases deviate from ideal gas behavior. (a) Using the van der Waals equation

Refrigerator Cycle and Coefficient of Performance

A refrigerator operates on a reversed Carnot cycle. (a) Draw a schematic diagram (P–V or T–S) of th

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

Thermal Equilibrium and the Zeroth Law

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

Thermal Equilibrium and the Zeroth Law

In an experiment, two objects (A and C) both have temperatures measured at $$300\;K$$. A third objec

Thermodynamic Process Comparison: Isothermal vs Adiabatic

Consider an ideal gas undergoing two different expansion processes: an isothermal expansion and an a

Thermodynamic Process Data Analysis: Evaluating P–V and T–S Diagrams

Graphs such as P–V and T–S diagrams provide insight into the energy changes in a system during therm

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 Heat Transfer in Different Thermodynamic Paths

A gas transitions from an initial state 'a' to a final state 'b' via two different paths on a P–V di

Work Done in Thermodynamic Processes

A gas undergoes two different expansion processes between the same initial and final states as descr

Application of Coulomb's Law

Coulomb’s Law states that the magnitude of the electric force between two point charges is given by

Balanced Forces: Charged Balloon in Combined Electric and Gravitational Fields

A student sets up an experiment to determine the charge required on a small balloon so that the upwa

Charge Quantization Experiment Analysis

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

Charge Redistribution between Conducting Spheres

Two conducting spheres are used in experiments to study charge distribution. Initially, both spheres

Charge Redistribution by Induction

Two initially neutral metallic spheres are suspended by insulating strings. A positively charged rod

Charge Redistribution via Induction

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

Charging and Discharging of a Capacitor – Time Response Analysis

This problem examines the time-dependent behavior of a capacitor in an RC circuit and requires you t

Comparison of Dipole and Monopole Field Mapping

A simulation experiment compares equipotential maps for a single point charge (monopole) and for a d

Comprehensive Analysis: Electric Field, Potential, and Energy

A comprehensive investigation is carried out on a system with a single point charge $$Q$$ fixed at t

Determining Capacitor Properties from Energy Storage

A parallel-plate capacitor stores a charge of 50 μC and has a capacitance of 10 nanofarads. The plat

Diagram Analysis: Electric Field Lines and Equipotentials in a Dipole

The following diagram represents an electric dipole configuration. It shows two charges located on t

Dielectric Effects in a Capacitor

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

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

Electric Field Line Patterns and Interpretation

Electric field lines provide a visual representation of the electric field in space. Analyze a given

Electric Field Lines at Media Boundaries

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

Electric Field Modeling in a Charged Particle Accelerator Element

In a charged particle accelerator, a pair of parallel plate electrodes is used to generate a uniform

Electric Field Variation with Distance

An experiment measures the magnitude of the electric field produced by a point charge as a function

Electric Force Sensor Alignment Experiment

A student uses an electric force sensor mounted on a pivot to measure the net force on a test charge

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

Energy Conservation in a Capacitor Discharge

A capacitor with a capacitance of 20 μF is initially charged to 200 V and then discharged through a

Equipotential Maps for a Dipole Configuration

An electric dipole consisting of charges $$+Q$$ and $$-Q$$ creates an intricate pattern of electric

Equipotential Surface Analysis in a Dipole Field

This question uses the mapping of equipotential surfaces in the vicinity of an electric dipole to ex

Equipotential Surfaces and Electric Field Lines

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

Force and Potential Energy in the Hydrogen Atom

For a hydrogen atom, consider the proton and electron separated by a distance of 0.5×10^-10 m. Using

Force Comparison in Hydrogen Atom

A researcher compares the electric and gravitational forces between the proton and electron in a hyd

Impact of Dielectrics on Capacitance

A recent report claims that inserting a dielectric with a dielectric constant of 3 into a parallel-p

Millikan Oil Drop Experiment Analysis

The Millikan oil drop experiment played a pivotal role in determining the fundamental charge of the

Non-Uniform Charge Distribution Effects

A researcher examines the electric field created by a hemispherical charge distribution with total c

Parallel-Plate Capacitor Design

A researcher aims to design a parallel-plate capacitor in vacuum. The desired capacitance is $$15 \;

Polarization Effects in Conductors vs. Insulators

A positively charged rod is brought near two initially uncharged spheres: Sphere A (a conductor) and

Potential Energy Change in a Non-Uniform Field

Consider a fixed point charge $$Q$$. A test charge $$q$$ moves from a distance $$r_A$$ to $$r_B$$ fr

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 Electric Fields: Square Charge Configuration

Four identical positive point charges are fixed at the vertices of a square with side length 0.20 m.

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

Surface Charge Distribution on Irregular Conductors

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

Uniform Electric Field Balance Experiment

A large, positively charged horizontal plate produces a uniform electric field of magnitude $$E = 1.

Work and Energy in a Non-Uniform Electric Field

A point charge $$q$$ is released from rest at a distance $$r_A$$ from a fixed charge $$Q$$. As $$q$$

Analyzing Power Dissipation with a Variable Resistor

A resistor with a variable resistance ranging from 5 Ω to 20 Ω is connected to a constant 12 V sourc

Analyzing Power Efficiency in Batteries with Internal Resistance

A battery with an EMF of 15 V and internal resistance $$r = 0.5\,Ω$$ is connected to a load resistor

Analyzing Series RC Circuit Transient Behavior

A series RC circuit is set up with a resistor and a capacitor connected to a 12 V battery. Initially

Analyzing Transients in RC Circuits with Switching

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

Battery Internal Resistance and Terminal Voltage Analysis

A battery with an electromotive force (EMF) of 12 V is modeled as an ideal voltage source in series

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

Circuit Design for Energy Efficiency

An engineer designs two circuits using the same 12 V battery but with different resistor network con

Comparative Energy Storage: Batteries vs Supercapacitors

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

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 through Experimental Measurements

A researcher studies a uniform wire made of an unknown material. The wire has a length of 2 m and a

Effect of Altering Capacitance on Circuit Response

Consider an RC circuit in two scenarios: one where the battery remains connected and one where the b

Impact of Internal Resistance on Battery Terminal Voltage

A battery with an emf of $$12 \text{ V}$$ and an internal resistance of $$2 \Omega$$ is connected to

Impact of Temperature on Battery Performance

Temperature can impact battery performance by altering its internal resistance.

Investigating Battery Internal Resistance using a Series Circuit

A student designs an experiment to measure the internal resistance (r) of a battery. The setup consi

Investigation of Capacitor-Battery Interaction under Variable Conditions

In an experiment, a capacitor is charged under two conditions: with the battery connected and with t

Investigation of Non-Ohmic Behavior

A filament lamp exhibits non-ohmic behavior. The following graph shows its voltage versus current re

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

Ohm's Law and Circuit Analysis

A circuit consists of an ideal battery with an EMF of 12 V and a resistor of 6 Ω. First, assume the

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

Ohm's Law in a Complex Circuit

A 9 V battery is connected to a resistor network. The network consists of a resistor R₁ = 50 Ω in se

Power Dissipation Optimization in Resistor Networks

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

Quantitative Analysis of Voltage Drops in a Multi-Loop Circuit

A complex circuit is built with two loops sharing a common resistor. The circuit includes two 12 V b

RC Circuit: Charging and Discharging of a Capacitor

A timing circuit consists of a resistor and a capacitor connected in series with a 12 V battery via

Resistor Combination Analysis: Series and Parallel

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

Resistor Network Analysis

Consider a circuit with multiple resistors arranged in series and parallel. The table below provides

Series and Parallel Circuit Analysis

In this problem, you will analyze a circuit that comprises a combination of resistors in both series

Switching Dynamics in Direct Current Circuits

Direct current circuits often include switches that change the circuit configuration. Consider a cir

Temperature Effects on Material Resistivity

The resistivity of a material is given by the formula $$\rho = \rho_0 [1 + \alpha (T - T_0)]$$. A wi

Transient and Steady State Analysis in RC Circuit

Consider an RC circuit with a resistor $$R = 1\times10^3\,\Omega$$, a capacitor $$C = 10\,\mu F$$, a

Understanding Charging and Discharging Curves of Capacitors

In an experiment, a capacitor is alternately charged by connecting it to a battery and then discharg

Analysis and Improvement of a Textbook Magnetic Field Diagram

A textbook diagram intended to illustrate the magnetic field around a bar magnet is provided. The di

Analysis of a Two-Component Magnetic Circuit

Consider a magnetic circuit composed of two adjacent materials (A and B) with different permeabiliti

Analysis of Motional EMF in a Moving Conductor

A metal rod of length $$\ell = 0.4 \; m$$ moves with a constant speed of $$v = 4 \; m/s$$ through a

Analysis of Solenoids: Field Uniformity and Enhancements

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

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

Calculating Magnetic Flux in a Non-Uniform Magnetic Field

A rectangular loop with width $$w = 0.2$$ m and height $$h = 0.3$$ m is placed in a magnetic field t

Charged Particle in a Uniform Magnetic Field

A positively charged particle with charge $$q = 2.0 * 10^{-6}$$ C enters a region with a uniform mag

Combined Effects of Electric and Magnetic Forces on a Moving Charge

A charged particle moves in a region with both uniform electric and magnetic fields. Analyze the mag

Dependence of Induced EMF on Rotation Rate

A circular loop rotates continuously in a uniform magnetic field, thereby inducing an emf that varie

Design of a Magnetic Braking System

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

Determining Magnetic Force on a Moving Charge

A researcher sets up an experiment where a charged particle is projected horizontally into a region

Electromagnetic Induction and Energy Conversion

This FRQ focuses on the conversion of mechanical energy into electrical energy via electromagnetic i

Experimental Determination of Magnetic Permeability

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

Faraday's Law and Rotating Loop

This FRQ requires applying Faraday's law to a rotating circular loop in a uniform magnetic field.

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 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

Impact of Magnetic Field Orientation on Faraday Induction

A square loop with area $$A = 0.1$$ m² rotates in a uniform magnetic field of $$B = 0.5$$ T. Answer

Induced EMF in a Rotating Loop

A circular loop rotates within a uniform magnetic field, causing the magnetic flux through the loop

Investigating Induced Current in a Loop with Changing Orientation

Design an experiment to investigate how changing the orientation of a loop relative to a magnetic fi

Investigating Induced EMF and Electrode Separation

An experiment investigates how the induced emf in a rod moving through a magnetic field changes with

Magnetic Dipoles: Bar Magnet and Current Loop

A researcher compares the magnetic field produced by a permanent bar magnet with that produced by a

Magnetic Field Mapping with Iron Filings

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

Magnetic Field Visualization and Field Lines

This FRQ addresses mapping magnetic fields using iron filings and interpreting the patterns observed

Magnetic Force on a Current-Carrying Conductor

A U-shaped wire is partially immersed in a uniform magnetic field. Parts of the wire experience diff

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

Measuring Magnetic Permeability via Compass Deflection

An experiment attempts to determine the magnetic permeability of a material by measuring the deflect

Measuring the Magnetic Field Inside a Solenoid

A solenoid in a laboratory has 500 turns and a length of $$L = 0.5 \; m$$ and carries a current of $

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 $$l = 0.5 \; m$$ moves with a constant velocity $$v = 3 \; m/s$$ through

Motional EMF in Non-Uniform Magnetic Fields

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

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

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

Temperature Effects on Magnetic Permeability in Materials

Researchers aim to study how temperature influences the relative magnetic permeability of ferromagne

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

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

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

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

Advanced Thin Lens Systems in Compound Microscopes

A compound microscope uses two converging lenses: an objective lens with a focal length of $$f_o = 0

Analyzing the Polarization of Electromagnetic Waves

Polarization describes the orientation of light waves. In this problem, you will explain polarizatio

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

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

Calculating Lens Power from Image Magnification

An object is placed $$10 \text{ cm}$$ in front of a converging lens and produces a real image that i

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

A researcher uses a concave mirror with a focal length of $$10$$ cm to study image formation. An obj

Converging Lens and Image Formation

Converging lenses project real images through refraction. Analyze an optical scenario involving a co

Converging Lens Magnification Experiment

A student performs an experiment with a converging (bi-convex) lens. In this setup, an object is pla

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

Convex Mirror Image Formation

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

Curved Mirror and Lens Combination in Optical Instruments

Design a simplified optical instrument that incorporates a concave mirror and a converging lens. Ans

Determining Indices and Critical Angles

Light travels from a glass medium into air. In one experiment, a beam in glass strikes the interface

Diffraction Grating Experiment: Determining Wavelength of Light

Design an experiment using a diffraction grating to determine the wavelength of a light source. Your

Diffraction Limits in Optical Instruments

The resolving power of optical instruments is limited by diffraction. Answer the following:

Diverging Lens Image Construction

A diverging lens has a focal length of $$-25\,cm$$. An object is placed $$50\,cm$$ in front of the l

Effect of Medium on EM Wave Propagation: Frequency Invariance Error Analysis

A student investigates the propagation of electromagnetic waves through air with varying humidity le

Electromagnetic Wave Generation and Analysis

An oscillating charge in an antenna generates electromagnetic waves. Consider a radio transmitter op

Electromagnetic Wave Interference and Phase Difference

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

Electromagnetic Wave Propagation: Error Analysis

A student designs an experiment to measure the speed of electromagnetic waves in a vacuum. The appar

Experimental Interference Pattern Analysis

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

Fiber Optic Communication Design

In fiber optic communication, light is guided through a cable by total internal reflection. Consider

Fiber Optics and Total Internal Reflection

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

Interference from Multiple Sources

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

Investigating Snell's Law: Relationship between Incident and Refraction Angles

Design an experiment to study the relationship between the angle of incidence and the angle of refra

Lens Power Calculation from Image Magnification

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

Medium Effects on Light Wavelength

When light enters a medium from a vacuum, its speed decreases while its frequency remains constant.

Multi-Wavelength Interference Experiment

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

Plane Mirror Image Characteristics

This question explores the properties of images formed by plane mirrors and asks you to explain why

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 Intensity of EM Waves

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

Polarization Effects in Electromagnetic Waves: Experiment Design

Design an experiment to investigate the effect of polarizing filters on the intensity of light. Your

Reflection and Refraction using Snell's Law

A beam of light in air (with $$n_{air} = 1.0$$) is incident upon a glass surface (with $$n_{glass} =

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

Single Slit Diffraction Analysis

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

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 and Image Formation

A concave spherical mirror has a radius of curvature of $$20 \text{ cm}$$. An object is placed $$10

Spherical Mirrors: Convex Mirror Analysis

A convex mirror is used in an experiment, and the following data on object distance, image distance,

The Doppler Effect for Electromagnetic Waves

In a laboratory experiment, the frequency of light from a moving source was measured under different

Total Internal Reflection

When light travels from water ($$n = 1.33$$) to air ($$n = 1.0$$), total internal reflection can occ

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: Measuring the Critical Angle between Water and Air

Design an experiment to determine the critical angle for total internal reflection at the water-air

Young's Double-Slit Experiment Analysis

In a Young's double-slit experiment, the slit separation is $$d = 1.5*10^{-3}\,m$$, the distance to