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 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 Over a Wing

An airplane wing has a surface area of 16 m². The pressure difference between the bottom and the top

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

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 Constricting Pipe

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

Bernoulli's Equation in Pipe Flow

A pump forces water through a horizontal pipe that includes a constriction. At Point 1 (just after t

Bernoulli's Pressure-Velocity Analysis

In a fluid dynamics experiment, water is pumped through a horizontal pipe that gradually narrows. Th

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 and Pressure Measurements

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

Buoyancy and Immersion Fraction

A homogeneous solid object has a mass of $$200$$ kg and a volume of $$1.0$$ m³. It is placed in two

Buoyancy and Submerged Volume

This problem focuses on buoyancy calculations using Archimedes’ principle and the concept of volume

Buoyancy and Submerged Volume of a Submarine

A submarine with a total volume of 300 m³ is designed to be neutrally buoyant in seawater (density $

Centrifugal Effects on Fluid Pressure Distribution

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

Column Pressure Experiment

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

Comparing Fluid Pressures in Different Media

Two open-top tanks contain different fluids. Tank 1 is filled with water (density = $$1000 \cdot kg/

Composite Material Density and Pressure Analysis

A materials scientist tests a new composite material by first measuring a 0.001 m³ sample with a mas

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 Experimental Variation

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

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

Continuity Equation in a Varying-Diameter Pipe

A fluid flows through a pipe that changes diameter along its length. At Section 1, the pipe has a ra

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:

Effect of Fluid Density on Buoyancy Force

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

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

Exploring Buoyancy in Variable Fluid Densities

A block with a volume of $$0.5\,m^3$$ and a mass of $$400\,kg$$ is placed in two different fluids. I

Exploring the Incompressibility Assumption in Fluids

Design an experiment to test the assumption of fluid incompressibility by comparing the behavior of

Flow in an Open Channel: Continuity and Energy Considerations

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

Flow Rate 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

Fluid Compressibility and Breakdown of Bernoulli's Equation

Bernoulli's equation assumes that fluids are incompressible. In high-speed flows, however, compressi

Fluid Exit Velocity: An Orifice Flow Experiment

A group of students conducts an experiment to measure the speed of water exiting a small orifice at

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 in an Open-Channel System: Integration of Concepts

A researcher conducts a comprehensive investigation of fluid flow in an open-channel system (e.g., a

Fluid Flow in Curved Pipes and Centrifugal Effects

In a chemical processing plant, fluid flows through a curved pipe. The curvature induces centrifugal

Fluid Flow Through Porous Media: Investigating Darcy's Law

Design an experiment to study the flow of a fluid through a porous medium (such as packed sand) and

Fluid Velocity and Pipe Cross-Section Experiment

According to the continuity equation, the product of cross-sectional area and velocity remains const

Hydraulic Press and Force Amplification

A hydraulic press consists of two pistons connected by an incompressible fluid. The larger piston ha

Hydrostatic Pressure and Density Experiment

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

Hydrostatic Pressure in a Fluid

Consider an open tank containing water. The water has a density of 1000 kg/m³. Atmospheric pressure

Hydrostatic Pressure Miscalculation Experiment

A student sets up an experiment to measure the pressure at the bottom of a water tank. The student f

Hydrostatic Pressure Variation

Consider a large open tank filled with water (density = 1000 kg/m³). The atmospheric pressure is giv

Inclined Pipe Flow with Incorrect Gravitational Component

A student analyzes fluid flow in an inclined pipe by measuring pressure at the upper and lower secti

Influence of Temperature on Fluid Density and Flow Characteristics

In some fluids, density varies with temperature according to the relation $$\rho = \rho_0 (1 - \beta

Investigating Fluid Pressure with a Manometer

A researcher employs a U-tube manometer to measure the gauge pressure in a pressurized system using

Measurement of Flow Rate in a Venturi Meter

A venturi meter is installed in a pipeline to measure flow rate by producing a pressure drop at the

Multi-Stage Fluid Dynamics Analysis in a Piping Network

A fluid flows through a piping network with three segments having different diameters and elevation

Object Buoyancy in Saltwater vs. Freshwater

An object with a density of $$600\;kg/m^3$$ is placed in two different fluids. In freshwater (densit

Pipe Flow and the Continuity Equation Experiment

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

Pipe Flow Continuity

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

Pressure Calculations in Submerged Structures

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

Pressure Distribution on a Submerged Plate

A researcher is studying the pressure distribution on a vertical rectangular plate submerged in wate

Pressure on a Vertical Column

A cylindrical concrete pillar has a base area of $$0.75\,m^2$$, a height of $$3.0\,m$$, and a densit

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 vs Dynamic Pressure in Pipe

An experiment was conducted to measure the pressure components in a streamlined flow within a horizo

Temperature Effects on Fluid Density

In an experiment, the density of water was measured at different temperatures. The results are shown

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°

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

Turbulent vs. Laminar Flow: Reynolds Number Misinterpretation

A student conducts an experiment to study the transition from laminar to turbulent flow in a pipe by

Viscosity Neglect in Pipeline Flow Rate Experiment

A student conducts an experiment to measure the volume flow rate of oil through a pipeline with sect

Visualization of Laminar Flow in Pipes

In an experiment designed to visualize the velocity profile of a fluid in a pipe, sensors are placed

Adiabatic Expansion and Temperature Change

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

Adiabatic Process Compression Experiment Error

A student conducts an experiment to study adiabatic compression in a gas contained within a piston-c

Analyzing Work Done in Different Thermodynamic Paths

A gas undergoes changes between states along two alternate paths on a P–V diagram. Path 1 is a const

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

Comparative Analysis of Convection and Radiation Heating

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

Conduction Heat Transfer: Experimental Design for Material Thermal Conductivity Measurements

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

Designing an Experiment on Thermal Conductivity Variation with Material

A laboratory experiment is conducted to compare the thermal conductivity of different materials usin

Determining Molecular Mass from Kinetic Data

A researcher conducts an experiment to determine the molecular mass of an unknown gas by measuring i

Effect of Molar Mass on Gas Velocity

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

Effect of Molecular Mass on RMS Velocity

The root-mean-square velocity of gas molecules is given by $$v_{rms} = \sqrt{\frac{3k_BT}{m}}$$. (a)

Effect of Temperature on rms Velocity

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

Entropy Change in a Heating Process

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

Entropy Changes in Thermodynamic Processes

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

Evaluating Experimental Error in the Ideal Gas Law Measurements

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

Evaluating Heat Transfer Mechanisms in a Fluid System

A fluid heating system employs both convection and radiation to transfer heat from a furnace to an a

First Law in a Cyclic Process

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

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

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

Force on Container Lid from Confined Gas

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

Gas Pressure Calculation and Net Force Analysis

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

Heat Capacity and Calorimetry

In calorimetry, the specific heat capacity of a substance is determined by measuring temperature cha

Heat Engine Efficiency

A heat engine operates in a cyclic process where heat is taken in from a high-temperature source, pa

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 and Energy Analysis

A heat engine operates in cycles, drawing heat from a high-temperature reservoir and rejecting part

Investigating the Role of Atmospheric Pressure in Sealed Container Systems

The net force on a container’s lid results from the difference between the internal gas pressure and

Isothermal Process Work Calculation

An ideal gas undergoes an isothermal expansion at a constant temperature of 350 K. The gas expands f

Maxwell-Boltzmann Distribution Analysis

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

Maxwell-Boltzmann Distribution Analysis Experiment Error

A student conducts an experiment to validate the Maxwell-Boltzmann distribution by measuring the fli

Modes of Heat Transfer: Conduction, Convection, and Radiation

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

Molecular Speed and Temperature

Consider an ideal gas composed of molecules each having mass m. The root‐mean‐square speed is given

Net Force on a Container Lid

A cylindrical container has a lid that is subjected to internal gas pressure from below and atmosphe

Phase Diagrams and Critical Points

Phase diagrams provide insight into the states of a pure substance under various conditions. (a) Des

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

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

Refrigeration Cycle and Coefficient of Performance

A refrigeration cycle removes heat from a cold reservoir using work. (a) Describe the basic steps of

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

Thermal Conductivity through Conduction

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

Thermal Insulation Effectiveness Experiment Error

A student conducts an experiment to test the effectiveness of different insulation materials by meas

Thermodynamics and Mechanical Work in an Automobile Engine

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

Work Calculation in Sequential Thermodynamic Processes

A gas undergoes a two-step process: an isobaric expansion followed by an isochoric heating. Using th

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

Capacitor Design Challenge

A parallel-plate capacitor is constructed with two metal plates separated by a distance of 0.2 mm in

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

Charge Induction in Connected Conducting Spheres

In an induction experiment, two neutral conducting spheres are brought into contact while a charged

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

Coulomb’s Law in Different Media

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

Coulomb’s Pendulum Experiment Error Analysis

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

Determining Coulomb's Constant Experiment

A series of measurements is conducted to determine Coulomb’s constant $$k$$ by measuring the force b

Determining Coulomb's Constant Experiment

A researcher conducts an experiment to determine Coulomb's constant by suspending two small charged

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

Electric Dipole Analysis

A researcher studies an electric dipole consisting of a positive charge of $$+4.0 \; nC$$ and a nega

Electric Field Due to a Uniformly Charged Rod

A thin rod of length 0.5 m carries a uniform linear charge density of $$\lambda = 2.0*10^{-6}$$ C/m.

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 from Four-Point Charges in a Square

Four identical positive point charges, each of magnitude $$5.0*10^{-9}$$ C, are placed at the vertic

Electric Field Lines and Equipotential Mapping Misinterpretation

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

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 Potential Dependence Experiment

An experiment is conducted to measure the electric potential at various distances from a fixed point

Electric Potential Due to a Point Charge

A point charge of $$+2.0*10^{-9}$$ C creates an electric potential in the surrounding space. (a) Ca

Electric Potential Energy in Uniform Field

A researcher moves a charge $$q$$ along the direction of a uniform electric field $$E$$. The displac

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$

Energy Storage in a Capacitor with a Dielectric Material

A capacitor with initial capacitance $$C_0$$ is charged to a voltage $$V_0$$. After charging, the ca

Equilibrium of an Object in a Uniform Electric Field

An object of mass 5 g is suspended in a uniform electric field of $$1.0*10^{6}$$ N/C such that the u

Equipotential Maps and Electric Field Lines for a Dipole

An equipotential map along with superimposed electric field lines for an electric dipole is provided

Equipotential Surfaces and Electric Field Lines

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

Fringing Fields in Parallel-Plate Capacitors

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

Induction Charging Experiment: Charge Redistribution Oversight

An experiment is conducted to study charging by induction using two initially uncharged metal sphere

Measuring Electric Potential Variations from a Point Charge

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

Potential Energy Change in a Uniform Field

In a controlled experiment, a charged particle initially at rest moves through a uniform electric fi

Proton–Electron Force Comparison in a Hydrogen Atom

In a hydrogen atom the proton and electron are separated by a Bohr radius of 0.5×10^-10 m. Given tha

Verification of Coulomb’s Law through Force Measurements

An experiment was conducted to verify Coulomb’s Law by measuring the electric force between two char

Voltmeter Experiment: Internal Resistance Oversight

A student designs an experiment to measure the electric potential difference between two points in a

Work Done and Change in Electric Potential Energy

A particle with charge $$q = +3.0 \times 10^{-9} \; C$$ is displaced by $$0.05 \; m$$ in the directi

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 a Real Battery’s Performance in a Resistive Circuit

A real battery with an EMF of 9 V and an internal resistance of 0.5 Ω is connected to a load resisto

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 Kirchhoff’s Laws in a Complex Circuit

A circuit is constructed with a 15 V battery that feeds into three branches: one with a 5 Ω 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

Assessing the Impact of Ammeter Internal Resistance

A student measures the current in a DC circuit by inserting an ammeter in series with a resistor and

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

Capacitor Charging in an RC Circuit

In an RC circuit, a capacitor is charged through a resistor by a 12 V battery. The voltage across th

Capacitor Combination Analysis

Two capacitors, one with $$10\,\mu F$$ and the other with $$20\,\mu F$$, are arranged in different c

Circuit Analysis with Multiple Voltage Sources

A circuit contains two batteries with EMFs of 12 V and 9 V connected in opposition (i.e., the positi

Comparing Conductor Materials: Effect on Efficiency

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

Designing a Circuit for a Specific Equivalent Resistance

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

Determination of Material Resistivity

A student is conducting an experiment to determine the resistivity of wires made from different mate

Determining Equivalent Resistance in Mixed Resistor Networks

A circuit is constructed using three resistors: one resistor of 100 \(\Omega\), one of 200 \(\Omega\

Effects of Altering Capacitance in a Charged Capacitor Circuit

A capacitor is first charged in a circuit with a battery connected, and then the battery is disconne

Evaluating Conductance and its Relationship to Resistance

Electrical conductance, the reciprocal of resistance, is an important parameter in circuit analysis.

Evaluating the Combination of Multiple Battery Cells on Circuit Performance

A student builds a circuit by connecting three battery cells in series to increase the output voltag

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

Kirchhoff's Circuit Analysis

A circuit consists of two loops sharing a common resistor. In Loop 1, a 9 V battery is connected in

Measuring Material Resistivity to Determine Conductivity

A student measures the resistance of several wire samples made from the same material, varying in le

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-Loop Circuit Analysis Using Kirchhoff’s Laws

A circuit consists of two loops sharing a common resistor. Loop 1 contains a battery of $$10 \text{

Multi-loop Circuit Analysis: Equivalent Resistance Calculation

Consider a circuit with two interconnected loops sharing a common resistor. Loop 1 contains a batter

Non-Ohmic Behavior in Real-World Devices

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

Parallel Resistors and Junction Rule Application

A 12 V battery is connected to a network of three parallel resistors with values $$R_1 = 30\,Ω$$, $$

Power Dissipation Analysis in Resistive Networks

Consider a circuit powered by a $$24 \text{ V}$$ battery. The circuit consists of a series resistor

Power Dissipation in Resistor Circuits

A resistor circuit is tested under various load conditions. The table below provides the measured vo

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 Analysis with Switch Operations

In an RC circuit with a switch, experimental measurements indicate that immediately after closing th

RC Circuit Capacitor Charging

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

RC Circuit Response and Steady State Behavior

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

RC Circuit Transients and Time Constants

An RC circuit is comprised of a resistor $$R = 5\times10^3\,\Omega$$ and a capacitor $$C = 2\,\mu F$

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

Resistivity and Material Properties Experiment

A student investigates the influence of material properties on resistance by measuring wires made of

Resistor Network Analysis

A circuit consists of three resistors. Resistor $$R_1$$ has a resistance of $$100\,\Omega$$ and is c

Terminal Voltage Variation Under Different Load Conditions

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

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

Analysis of Experimental Data in a Motional EMF Investigation

In an experiment, a sliding conductor is moved through a uniform magnetic field at various speeds, a

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

Analyzing Induced EMF with Sinusoidal Variation

Consider a loop in which the magnetic flux varies sinusoidally over time, described by $$\Theta_B(t)

Assessing Magnetic Permeability Effects

This FRQ explores how the magnetic permeability of materials influences the magnetic field generated

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

Calculating Magnetic Force on a Moving Charge

A charged particle moves through a uniform magnetic field. Use the information provided to answer th

Deflection of Charged Particles in Crossed Fields

In an experiment, charged particles are passed through a region where perpendicular electric and mag

Design and Optimization of an Electromagnet

A student is tasked with designing an electromagnet using a solenoid to generate a target magnetic f

Designing a Magnetic Levitation Experiment

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

Designing an Electromagnet with a Solenoid

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

Effect of Magnetic Field Strength on Induced Current

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

Effect of Material's Magnetic Permeability

Magnetic permeability is a material property that affects how a material responds to an external mag

Energy Dissipation in Resistive Magnetic Systems

An experiment investigates energy dissipation in a circuit where an induced current flows through a

Energy Storage in an Inductor

In an electrical circuit, an inductor with inductance $$L = 0.5 H$$ carries a current of $$I = 3 A$$

Exploration of Magnetic Flux Through a Rotating Loop

A circular loop of radius 0.03 m is placed in a uniform magnetic field of 0.2 T and rotated from 0°

Faraday’s Law and the Rotating Loop

A circular loop of radius 0.05 m rotates in a uniform magnetic field of 0.3 T. The loop rotates with

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 Comparison: Permanent vs. Electromagnets

In a laboratory experiment, the attractive force between a fixed magnet and a piece of iron is measu

Induced Current in a Sliding Rod Circuit

This FRQ examines the induction of current in a circuit containing a sliding rod on rails and evalua

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

Magnetic Field Lines Visualization

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

Magnetic Field Visualization and Field Lines

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

Magnetic Flux Through a Rotating Loop

A circular loop of radius $$r = 0.03 \; m$$ is placed in a uniform magnetic field of strength $$B =

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

Magnetic Force on Moving Charge Experiment

A group of students designs an experiment to measure the magnetic force on electrons that are emitte

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

Measurement of Magnetic Fields Using Hall Effect Sensors

The Hall Effect is a valuable tool for measuring magnetic fields. Explain the principle behind Hall

Measuring Magnetic Permeability via Compass Deflection

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

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 Analysis

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

Motional EMF in a Sliding Rod

A conducting rod moving through a uniform magnetic field experiences a motional electromotive force

Radius of Circular Motion vs. Velocity

In a controlled experiment, charged particles are injected into a uniform magnetic field and follow

Solenoid Magnetic Field Measurement Experiment

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

Testing Lenz's Law with a Falling Magnet Through a Coil

An experiment involves dropping a magnet through a coil and measuring the induced current. The claim

Theoretical Exploration of Hypothetical Magnetic Monopoles

Although magnetic monopoles have not been observed, suppose that a magnetic monopole with magnetic c

Torque on a Current Loop in a Magnetic Field

A rectangular current loop is suspended in a uniform magnetic field. Its angular deflection is measu

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

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

Concave Mirror Image Analysis

An object of height $$h_o = 4 \ cm$$ is placed at a distance of $$d_o = 30 \ cm$$ in front of a conc

Convex Mirror Image Analysis

A researcher is examining a convex mirror. An object of height 5 cm is placed 40 cm in front of a co

Determining Index of Refraction Using Critical Angle Measurements

A student conducts an experiment to determine the index of refraction of a transparent material by m

Determining Slit Separation from Fringe Spacing

In a Young's double slit experiment, the measured fringe spacing on the screen is $$\Delta y = 2.5 \

Diffraction Grating Analysis

A diffraction grating with 5000 lines per centimeter is used to analyze light of wavelength $$650*10

Diffraction Gratings

A diffraction grating with 5000 lines per centimeter is illuminated by monochromatic light of wavele

Electromagnetic Wave Oscillation Diagram Analysis

Using the provided diagram showing oscillating electric (E) and magnetic (B) fields of an electromag

Electromagnetic Wave Oscillations

Describe how an oscillating charge produces an electromagnetic wave and explain the relationship bet

Electromagnetic Wave Propagation Analysis

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

Experimental Evaluation of the Electromagnetic Spectrum

Researchers often use a variety of techniques to measure the properties of electromagnetic radiation

Experimental Verification of the Law of Reflection

The law of reflection states that the angle of incidence equals the angle of reflection. This questi

Exploring the Relationship Between Frequency and Wavelength

A student conducts an experiment to examine the relationship between frequency and wavelength in dif

Image Formation by Concave Mirrors

A concave mirror has a focal length of $$10\,cm$$. An object of height $$4\,cm$$ is placed $$30\,cm$

Impact of Coherence on Interference Patterns

Coherence is crucial for the formation of clear interference patterns. Answer the following:

Interference and Phase Difference in Wave Superposition

Consider two coherent light waves with a constant phase difference.

Interference from Multiple Sources

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

Interference in Multiple-Slit Systems

An experiment compares the interference patterns produced by a double-slit setup and a triple-slit s

Interference Patterns and Young's Double Slit Experiment

An experiment using Young's double-slit setup produced the table below showing fringe positions. Ass

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

Optical Data Analysis from Spherical Mirror Measurements

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

Optical Fibers and Total Internal Reflection

Optical fibers use total internal reflection to guide light over long distances. Consider an optical

Photon Energy Calculation in the Electromagnetic Spectrum

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

Plane Mirror Image Formation

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

Plane Mirror Image Formation and Analysis

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

Radiation Pressure and Electromagnetic Waves

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

Radio Wave Wavelength Determination

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

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: Snell's Law

A beam of light traveling in air (with an index of refraction, n = 1.0) strikes a glass surface (n =

Reflection and Refraction: Snell's Law Experiment

A researcher directs a beam of light from air (index $$n_1 = 1.0$$) into a glass block with an index

Single Slit Diffraction Analysis

A single slit with width $$a = 0.20 \text{ mm}$$ is illuminated by monochromatic light of wavelength

Single Slit Diffraction Analysis

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

Single Slit Diffraction Analysis

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

Spherical Mirrors - Convex Mirror Analysis

An object of height 5 cm is placed 20 cm in front of a convex mirror with a focal length of -15 cm.

Spherical Mirrors: Concave Mirror Ray Tracing

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

The Doppler Effect for Electromagnetic Waves

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

Thin Lenses - Diverging Lens Analysis

An object of height 11 cm is placed 48 cm from a diverging lens with a focal length of -24.5 cm. (a

Total Internal Reflection in Prisms

A triangular prism made of glass with an index of 1.6 is used to redirect a light beam. A light ray

Calculating Nuclear Binding Energy

A researcher is investigating the stability of nuclei by calculating the nuclear binding energy per

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