Unit 16 - Grade 11-12 Physics

Magnetism, Induction, and Modern Physics

Study magnetic fields, magnetic force, motors, electromagnets, electromagnetic induction, Faraday's law, Lenz's law, generators, transformers, quantum ideas, atomic models, nuclear physics, and relativity basics.

Lesson roadmap

What Students Should Master in This Unit

This final unit connects electricity to magnetism, explains how changing magnetic fields generate electricity, and introduces the modern physics ideas behind atoms, photons, nuclei, and high-speed motion.

Analyze magnetic interactions

Use magnetic field direction, right-hand rules, forces on charges, forces on wires, and motor torque.

Explain electromagnetic induction

Connect magnetic flux, Faraday's law, Lenz's law, generators, transformers, and energy conservation.

Apply modern physics models

Use photon energy, photoelectric effect, atomic energy levels, nuclear equations, half-life, and relativity basics.

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Jump to a Topic

Magnetic Fields Field Lines Moving Charges Current-Carrying Wires Motors and Torque Electromagnets Magnetic Flux Faraday's Law Lenz's Law Generators and Transformers Modern Physics Photoelectric Effect Atoms and Matter Waves Nuclear Physics Relativity Basics Simulation Labs Lab Skills Worked Examples Practice Problems
Magnetic interaction model

1. Magnetic Fields

A magnetic field is a region where magnets, moving charges, or current-carrying wires experience magnetic force. Magnetic fields are vector fields, so direction matters as much as magnitude.

Current creates circular magnetic field lines wire I out of page bar magnet source N S right-hand rule: thumb = current curled fingers = B B = μ0I/(2πr)
Magnetic fields come from magnets and electric current; around a straight wire the field forms circles whose direction is found by the right-hand rule.
Magnetic field unit 1 T = 1 N/(A m) T stands for tesla.
Field around long straight wire B = μ0I/(2πr) Field circles around the wire.
Permeability of free space μ0 = 4π × 10-7 T m/A Constant used in many magnetism formulas.

Important Sources of Magnetic Field

  • Permanent magnets.
  • Moving electric charges.
  • Current-carrying wires.
  • Coils and solenoids.
  • Changing electric fields in advanced electromagnetic wave models.
Visualizing magnetic direction

2. Magnetic Field Lines

Magnetic field lines show the direction a north magnetic pole would point. Outside a bar magnet, field lines point from north to south. Inside the magnet, they continue from south to north, forming closed loops.

Bar magnet field lines N S outside magnet: field points N to S
Bar Magnet FieldMagnetic field lines form closed loops and are closest where the field is strongest.
Positive charge in B into page + v B into page FB
Right-Hand RuleFor a positive charge, point fingers with velocity, curl toward magnetic field, and thumb gives force direction.
Changing flux induces current N S motion A coil
Electromagnetic InductionMoving a magnet changes flux through the coil, inducing EMF and current if the circuit is closed.
Force on moving charged particles

3. Magnetic Force on Moving Charges

A magnetic field exerts force on a charge only when the charge is moving and has velocity component perpendicular to the magnetic field.

Magnetic force is perpendicular to velocity + v FB B into page circular motion when v ⊥ B
For a moving charge, magnetic force is perpendicular to both velocity and magnetic field; for negative charges, reverse the right-hand-rule force direction.
Magnetic force magnitude FB = |q|vB sinθ θ is angle between velocity and magnetic field.
Maximum magnetic force Fmax = |q|vB When velocity is perpendicular to field.
Circular path radius r = mv/(|q|B) Applies when v is perpendicular to uniform B.

Direction Rules

  • For positive charge, use the right-hand rule directly.
  • For negative charge, force direction is opposite the right-hand-rule result.
  • If v is parallel or antiparallel to B, magnetic force is zero.
  • Magnetic force is perpendicular to velocity, so it can change direction of motion without doing work.
Magnetic force on conductors

4. Force on Current-Carrying Wires

A current-carrying wire in a magnetic field can experience a force because moving charges in the wire experience magnetic forces.

Current-carrying wire in a magnetic field current I force F = ILB sinθ
A wire segment in a magnetic field experiences force when the current has a component perpendicular to the field.
Force on straight wire F = ILB sinθ L is wire length inside the magnetic field.
Maximum force Fmax = ILB When current is perpendicular to the magnetic field.
Field from current loop center B = μ0NI/(2R) For N circular turns of radius R at the center.

Wire Force Checklist

  • Identify current direction, not electron flow direction.
  • Identify magnetic field direction.
  • Use right-hand rule for current: fingers current, curl toward B, thumb force.
  • If wire is parallel to field, force is zero.
Turning magnetic force into motion

5. Motors and Magnetic Torque

Electric motors use magnetic forces on current-carrying loops to create torque. The loop turns because opposite sides of the loop experience forces in opposite directions.

Motor effect: opposite wire forces create torque N S torque F F
A motor loop turns because forces on opposite sides act in opposite directions, producing a torque.
Torque on current loop τ = NIAB sinθ N turns, current I, area A, magnetic field B.
Magnetic moment μ = NIA Direction found by right-hand rule around the loop.
Loop torque form τ = μB sinθ Same idea written using magnetic moment.

Motor Ideas

  • Motors convert electrical energy into mechanical energy.
  • A commutator can reverse current every half-turn to keep torque in a useful direction.
  • Larger current, more turns, larger loop area, or stronger field increases torque.
Magnetism from current

6. Electromagnets and Solenoids

An electromagnet is created when electric current produces a magnetic field. A solenoid is a coil of wire that acts like a bar magnet when current flows.

Solenoid: a coil becomes an electromagnet strong field inside coil more turns + more current + iron core = stronger electromagnet
A solenoid concentrates magnetic field through its center; increasing current, turns, or adding an iron core strengthens the electromagnet.
Solenoid field B = μ0nI n is turns per meter for a long ideal solenoid.
Turns per length n = N/L More turns per meter strengthens field.
Magnetic field energy idea energy stored in field Inductors store energy in magnetic fields in advanced circuit models.

Strengthening an Electromagnet

  • Increase current.
  • Increase number of coil turns.
  • Use an iron core.
  • Make coil turns closer together.
Magnetic field through area

7. Magnetic Flux

Magnetic flux measures how much magnetic field passes through a surface. Induction depends on changing flux, not simply on the presence of a magnetic field.

Magnetic flux depends on B, area, and angle area normal B field ΦB = BA cosθ
Flux is largest when the magnetic field is perpendicular to the loop area and zero when the field is parallel to the surface.
Magnetic flux ΦB = BA cosθ θ is angle between B and area normal.
Flux unit 1 Wb = 1 T m2 Wb stands for weber.
Ways to change flux change B, A, or θ Any changing flux can induce EMF.

Flux Intuition

  • Maximum flux occurs when field is perpendicular to the loop area.
  • Zero flux occurs when field is parallel to the loop surface.
  • Changing orientation can induce EMF even if field strength stays constant.
Changing flux creates EMF

8. Faraday's Law

Faraday's law says that a changing magnetic flux through a circuit induces an electromotive force. If the circuit is closed, the induced EMF can drive current.

Faraday's law: faster flux change gives larger EMF N S motion A ε = -NΔΦ/Δt
Moving the magnet faster or using more coil turns increases the magnitude of the induced EMF.
Faraday's law ε = -NΔΦB/Δt N is number of coil turns.
Induced current I = ε/R If the circuit resistance is R.
Motional EMF ε = BLv For a rod of length L moving perpendicular to B.

What Increases Induced EMF?

  • More coil turns.
  • Faster change in magnetic field.
  • Larger loop area.
  • Faster motion of a magnet, coil, or conducting rod.
Direction of induced current

9. Lenz's Law

Lenz's law gives the direction of induced current: the induced current creates a magnetic field that opposes the change in magnetic flux that caused it.

Lenz's law: induced field opposes the change N S opposing B induced current direction incoming north pole increases flux, so coil acts like a north pole to oppose it
Lenz's law is an energy-conservation rule: the induced current resists the change that produced it.
Lenz's law sign negative sign in Faraday's law Induced effects oppose flux change.
Energy conservation opposes the change Prevents free energy from induction.
Direction method change -> oppose -> current Decide flux change first, then induced field, then current.

Step-by-Step Lenz Reasoning

  1. Choose the loop or coil surface.
  2. Find the original magnetic flux direction through the loop.
  3. Decide whether that flux is increasing or decreasing.
  4. Choose induced magnetic field that opposes the change.
  5. Use right-hand rule to find induced current direction.
Electromagnetic technology

10. Generators and Transformers

Generators convert mechanical energy into electrical energy by induction. Transformers use changing magnetic flux to change AC voltage levels.

Induction technology: generators and transformers N S generator coil rotates transformer core Vs/Vp = Ns/Np
Generators use motion to change flux; transformers use changing AC flux between coils to step voltage up or down.
Transformer voltage ratio Vs/Vp = Ns/Np Ideal transformer relation.
Transformer current ratio Is/Ip = Np/Ns Current changes inversely to voltage in ideal model.
Ideal power Pp = Ps Real transformers lose some energy as heat and sound.

Applications

  • Electric generators in power plants.
  • Transformers in power transmission.
  • Wireless charging and induction cooktops.
  • Electric guitar pickups and microphones.
  • Magnetic braking and eddy currents.
Physics beyond the classical model

11. Modern Physics Overview

Modern physics explains phenomena that classical mechanics and classical electromagnetism cannot fully describe, especially at atomic scales, nuclear scales, and speeds close to light speed.

Modern physics connects quantum, nuclear, and high-speed ideas atoms and energy levels nuclei and radiation near light speed relativity
Modern physics adds models for quantized energy, nuclear reactions, and objects moving near the speed of light.
Area Core Question Student Takeaway
Quantum physicsHow do light and matter behave at small scales?Energy can be quantized; light has photon behavior.
Atomic physicsHow are electrons arranged in atoms?Atoms have discrete energy levels.
Nuclear physicsWhat happens inside atomic nuclei?Mass can convert to energy in nuclear reactions.
RelativityWhat happens near light speed?Time, length, and energy behave differently at high speeds.
Light as particles

12. Photoelectric Effect

The photoelectric effect occurs when light ejects electrons from a metal. Classical wave theory could not explain the threshold frequency, but photon theory can.

Photoelectric effect: photons eject electrons metal plate photon, E = hf emitted electron Kmax = hf - φ
Electron emission depends on photon frequency, not just brightness; below threshold frequency no electrons are emitted.
Photon energy E = hf h is Planck's constant.
Photon energy with wavelength E = hc/λ Shorter wavelength means higher photon energy.
Photoelectric equation Kmax = hf - φ φ is work function of the metal.

Photoelectric Observations

  • Below threshold frequency, no electrons are ejected no matter how bright the light is.
  • Above threshold frequency, increasing frequency increases electron kinetic energy.
  • Above threshold frequency, increasing intensity increases number of emitted electrons.
  • Electron emission is nearly immediate when photon energy is high enough.
Quantized matter and energy

13. Atomic Models and Matter Waves

Atomic physics explains spectra, energy levels, and electron behavior. Matter also has wave properties, especially noticeable for tiny particles like electrons.

Atomic spectra come from energy-level transitions n = 1 n = 2 n = 3 photon ΔE = hf λ = h/p for matter waves
Atoms emit or absorb photons when electrons move between discrete energy levels; tiny particles also have matter-wave behavior.
de Broglie wavelength λ = h/p p is momentum.
Energy-level photon ΔE = hf Photon energy matches energy-level difference.
Hydrogen energy level En = -13.6 eV/n2 Common simplified model for hydrogen.

Atomic Model Ideas

  • Rutherford scattering showed atoms are mostly empty space with a tiny dense nucleus.
  • Bohr's model introduced quantized electron energy levels for hydrogen.
  • Emission spectra occur when electrons drop to lower energy levels and emit photons.
  • Absorption spectra occur when electrons absorb photons with matching energy.
Energy inside nuclei

14. Nuclear Physics

Nuclear physics studies protons, neutrons, isotopes, radioactivity, fission, fusion, and mass-energy conversion.

Nuclear physics: decay, fission, fusion, and mass-energy α, β, or γ fission releases neutrons and energy E = mc2
Nuclear reactions can transform nuclei and release energy because a small amount of mass corresponds to a large amount of energy.
Mass-energy equivalence E = mc2 Small mass changes can release large energy.
Half-life model N = N0(1/2)t/T T is half-life.
Activity idea activity decreases over time Fewer undecayed nuclei means lower decay rate.

Radioactive Decay Types

Decay What Leaves Nucleus Change to Atomic Number
Alpha (α)Helium nucleusAtomic number decreases by 2.
Beta minus (β-)Electron and antineutrinoAtomic number increases by 1.
Beta plus (β+)Positron and neutrinoAtomic number decreases by 1.
Gamma (γ)High-energy photonAtomic number stays the same.

Fission and Fusion

  • Fission: a heavy nucleus splits into lighter nuclei, often releasing neutrons and energy.
  • Fusion: light nuclei combine into a heavier nucleus, releasing energy when products are more tightly bound.
  • Nuclear reactors use controlled fission chain reactions.
  • Stars release energy mainly through fusion.
High-speed physics

15. Relativity Basics

Special relativity becomes important when objects move at speeds close to the speed of light. Grade 11-12 courses often focus on the concepts and a few core formulas.

Relativity matters when speed is close to c v near c moving clocks run slow γ = 1/√(1 - v2/c2)
As speed approaches the speed of light, time dilation, length contraction, and mass-energy equivalence become important.
Speed of light c = 3.00 × 108 m/s Same for all inertial observers in vacuum.
Lorentz factor γ = 1/√(1 - v2/c2) Grows large as v approaches c.
Relativistic energy idea Erest = mc2 Rest mass corresponds to rest energy.

Relativity Concepts

  • Time dilation: moving clocks are measured to run slow by an observer.
  • Length contraction: objects moving near light speed are measured shorter along the motion direction.
  • No object with mass can be accelerated to exactly light speed.
  • Mass-energy equivalence connects relativity to nuclear physics.
Simulation labs

16. Simulation Labs for This Unit

These PhET simulations help students visualize magnetic fields, induction, generators, quantum effects, atomic models, and nuclear processes.

Use simulations to connect models, measurements, and explanations predict field/current manipulate B, coil turns, f explain evidence + formula repeat with one variable changed
Strong simulation work changes one variable at a time, records evidence, and connects observations to formulas.
Magnets and Electromagnets

Explore bar magnets, compass direction, field strength, electromagnets, coils, and current direction.

Lab idea: reverse current in an electromagnet and observe the field direction change.
Open Simulation
Faraday's Law

Move magnets and coils to see how changing magnetic flux induces current.

Lab idea: compare slow and fast magnet motion through a coil.
Open Simulation
Generator

Investigate how mechanical motion, magnetic fields, coils, and current connect in generators.

Lab idea: explain how faster rotation changes induced current.
Open Simulation
Photoelectric Effect

Test threshold frequency, photon energy, light intensity, emitted electrons, and stopping voltage.

Lab idea: change frequency and intensity separately and compare results.
Open Simulation
Rutherford Scattering

Model alpha-particle scattering to understand evidence for a small dense nucleus.

Lab idea: compare plum pudding predictions with nuclear atom predictions.
Open Simulation
Build an Atom

Construct atoms and isotopes using protons, neutrons, and electrons.

Lab idea: change neutron number and identify isotope changes.
Open Simulation
Nuclear Fission

Explore fission, chain reactions, neutron release, and energy transfer in nuclear processes.

Lab idea: compare controlled and uncontrolled chain reactions conceptually.
Open Simulation
Investigation skills

17. Lab Skills for This Unit

This unit mixes hands-on field observations, circuit measurements, induction demonstrations, and modern physics data analysis. Clear diagrams and careful direction conventions matter.

Lab habit: draw directions before calculating N S A motion B direction label current, field, force, motion, coil turns, and meter polarity
Before measuring or calculating, label the directions of current, magnetic field, force, motion, and induced current.

Common Labs

  • Mapping magnetic field lines using compasses around bar magnets.
  • Right-hand rule practice for moving charges, wires, and coils.
  • Magnetic force on a current-carrying wire demonstration.
  • Electromagnet strength investigation using current, turns, and core material.
  • Faraday's law lab using coils, magnets, galvanometers, or simulations.
  • Transformer voltage ratio investigation with safe low-voltage AC equipment.
  • Photoelectric effect simulation lab for threshold frequency and stopping voltage.
  • Half-life data modeling using coins, dice, candies, or simulations.

Good Data Habits

  • Draw current, magnetic field, and force directions before calculating.
  • Label whether a field is into the page, out of the page, left, right, up, or down.
  • Use consistent units: tesla, meters, seconds, coulombs, amps, volts, joules, electronvolts.
  • Track signs carefully in induction and nuclear equations.
  • For modern physics, convert eV to joules only when needed.
Safety note: Use only teacher-approved magnets, coils, power supplies, and low-voltage equipment. Nuclear and photoelectric topics should be explored with simulations or approved classroom materials only.
Worked examples

18. Worked Examples

Example 1: Magnetic force on charge

A +2.0 µC charge moves at 3.0 × 105 m/s perpendicular to a 0.40 T field. Find force magnitude.

F = |q|vB = (2.0 × 10-6)(3.0 × 105)(0.40) = 0.24 N.

Example 2: Magnetic force angle

A charge moves at 2.0 × 106 m/s through B = 0.30 T at 30°. q = 1.6 × 10-19 C. Find force.

F = qvB sinθ = (1.6 × 10-19)(2.0 × 106)(0.30)sin30° = 4.8 × 10-14 N.

Example 3: Circular radius

A proton moves perpendicular to a 0.20 T field at 1.0 × 106 m/s. Find circular path radius.

r = mv/(qB) = (1.67 × 10-27)(1.0 × 106)/[(1.60 × 10-19)(0.20)] = 0.052 m.

Example 4: Force on wire

A 0.50 m wire carries 4.0 A perpendicular to a 0.25 T field. Find force.

F = ILB = (4.0)(0.50)(0.25) = 0.50 N.

Example 5: Solenoid field

A long solenoid has 800 turns/m and current 2.0 A. Find B.

B = μ0nI = (4π × 10-7)(800)(2.0) = 2.0 × 10-3 T.

Example 6: Magnetic flux

A 0.020 m2 loop is perpendicular to a 0.30 T field. Find flux.

ΦB = BA cos0° = (0.30)(0.020) = 6.0 × 10-3 Wb.

Example 7: Faraday's law

A 50-turn coil changes flux from 0.020 Wb to 0.005 Wb in 0.10 s. Find induced EMF magnitude.

|ε| = N|ΔΦ|/Δt = 50(0.015)/0.10 = 7.5 V.

Example 8: Motional EMF

A 0.40 m rod moves at 5.0 m/s perpendicular to B = 0.60 T. Find EMF.

ε = BLv = (0.60)(0.40)(5.0) = 1.2 V.

Example 9: Transformer voltage

A transformer has Np = 200 turns, Ns = 1000 turns, and Vp = 12 V. Find Vs.

Vs/12 = 1000/200 = 5, so Vs = 60 V.

Example 10: Photon energy

Find energy of a photon with frequency 5.0 × 1014 Hz.

E = hf = (6.63 × 10-34)(5.0 × 1014) = 3.32 × 10-19 J.

Example 11: Photoelectric effect

Light has photon energy 4.0 eV and metal work function is 2.3 eV. Find maximum electron kinetic energy.

Kmax = hf - φ = 4.0 - 2.3 = 1.7 eV.

Example 12: de Broglie wavelength

An electron has momentum 3.0 × 10-24 kg m/s. Find its wavelength.

λ = h/p = (6.63 × 10-34)/(3.0 × 10-24) = 2.21 × 10-10 m.

Example 13: Half-life

A sample starts with 80 g and has half-life 5 days. How much remains after 15 days?

15 days is 3 half-lives. Amount = 80(1/2)3 = 10 g.

Example 14: Mass-energy

A nuclear reaction converts 2.0 × 10-6 kg of mass into energy. Find energy released.

E = mc2 = (2.0 × 10-6)(3.00 × 108)2 = 1.8 × 1011 J.

Independent practice

19. Practice Problems

Try each problem first. Then open the answer check and compare formulas, directions, units, and signs.

1. A +3.0 µC charge moves at 2.0 × 105 m/s perpendicular to B = 0.50 T. Find force.

Answer

F = qvB = 0.30 N.

2. What is magnetic force if a charge moves parallel to a magnetic field?

Answer

Zero, because sin0° = 0.

3. A 0.80 m wire carries 2.5 A perpendicular to a 0.40 T field. Find force.

Answer

F = ILB = (2.5)(0.80)(0.40) = 0.80 N.

4. A wire is parallel to a magnetic field. What is force on the wire?

Answer

Zero.

5. A solenoid has n = 1200 turns/m and I = 1.5 A. Find B.

Answer

B = μ0nI = (4π × 10-7)(1200)(1.5) = 2.26 × 10-3 T.

6. List two ways to strengthen an electromagnet.

Answer

Increase current, add more coil turns, use an iron core, or tighten coil spacing.

7. A loop has A = 0.050 m2, B = 0.20 T, and angle 0° to the area normal. Find flux.

Answer

ΦB = BA = 0.010 Wb.

8. A 100-turn coil changes flux by 0.030 Wb in 0.50 s. Find induced EMF magnitude.

Answer

|ε| = NΔΦ/Δt = 100(0.030)/0.50 = 6.0 V.

9. What does Lenz's law say about induced current direction?

Answer

It creates a magnetic field that opposes the change in magnetic flux.

10. A 0.25 m rod moves at 8.0 m/s perpendicular to B = 0.30 T. Find motional EMF.

Answer

ε = BLv = (0.30)(0.25)(8.0) = 0.60 V.

11. A transformer has 500 primary turns and 250 secondary turns. If Vp = 120 V, find Vs.

Answer

Vs = 120(250/500) = 60 V.

12. Is the transformer in problem 11 step-up or step-down?

Answer

Step-down, because secondary voltage is lower.

13. Find photon energy for f = 6.0 × 1014 Hz.

Answer

E = hf = (6.63 × 10-34)(6.0 × 1014) = 3.98 × 10-19 J.

14. In the photoelectric effect, what happens if light frequency is below threshold?

Answer

No electrons are emitted, regardless of intensity.

15. Photon energy is 5.0 eV and work function is 2.0 eV. Find Kmax.

Answer

Kmax = 3.0 eV.

16. What does increasing light intensity do above threshold frequency?

Answer

It increases the number of emitted electrons, not their maximum kinetic energy.

17. An electron changes energy levels by 2.4 eV. What is the emitted photon energy?

Answer

2.4 eV.

18. What did Rutherford scattering show about the atom?

Answer

The atom has a small, dense, positively charged nucleus and is mostly empty space.

19. A sample has half-life 3 h. What fraction remains after 9 h?

Answer

9 h is 3 half-lives, so (1/2)3 = 1/8 remains.

20. In alpha decay, how does atomic number change?

Answer

It decreases by 2.

21. In beta minus decay, how does atomic number change?

Answer

It increases by 1.

22. Find energy from mass conversion of 1.0 × 10-8 kg.

Answer

E = mc2 = (1.0 × 10-8)(3.00 × 108)2 = 9.0 × 108 J.

23. What happens to Lorentz factor as speed approaches c?

Answer

It increases greatly and approaches infinity as v approaches c.

24. In the Faraday's Law simulation, what should happen when the magnet moves faster through the coil?

Answer

The induced EMF/current magnitude increases because flux changes faster.

Final review

20. What to Know Before Moving On

  • Magnetic fields are vector fields measured in tesla.
  • Magnetic field lines form closed loops and are closest where the field is strongest.
  • Magnetic force on moving charge is FB = |q|vB sinθ.
  • Magnetic force on a current-carrying wire is F = ILB sinθ.
  • Magnetic force is zero when motion or current is parallel to the magnetic field.
  • Motors use magnetic force on current loops to create torque.
  • Solenoid field is B = μ0nI for an ideal long solenoid.
  • Magnetic flux is ΦB = BA cosθ.
  • Faraday's law is ε = -NΔΦB/Δt.
  • Lenz's law says induced current opposes the change in flux.
  • Transformers follow Vs/Vp = Ns/Np in the ideal model.
  • Photon energy is E = hf = hc/λ.
  • The photoelectric effect follows Kmax = hf - φ.
  • Matter wavelength is λ = h/p.
  • Nuclear processes can convert mass to energy using E = mc2.
  • Half-life follows N = N0(1/2)t/T.
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