Skip to main content

Magnetism and Electromagnetic Induction

Subject: Physics
Topic: 7
Cambridge Code: 0625

Magnetic Fields​

Magnetic field - Region where magnetic force acts

Field Representation​

Magnetic field lines:

  • Direction: North to South pole (outside magnet)
  • Density indicates field strength
  • Never cross

Unit: Tesla (T) = kilograms/(Ampere·second²)

Magnetic Flux Density​

B=FILB = \frac{F}{IL}

Where:

  • F = force
  • I = current
  • L = length of conductor

Forces on Current-Carrying Conductors​

Force on conductor in magnetic field:

F=BILsin⁡θF = BIL\sin θ

Where:

  • B = magnetic flux density
  • I = current
  • L = length of conductor
  • θ = angle between B and L

Maximum force: θ = 90° (perpendicular) F=BILF = BIL

Zero force: θ = 0° or 180° (parallel or antiparallel)

Direction (Fleming's Left-Hand Rule)​

Thumb: Force direction First finger: Field direction Second finger: Current direction

Charges in Magnetic Fields​

Force on moving charge:

F=Bqvsin⁡θF = Bqv\sin θ

Where:

  • q = charge
  • v = velocity
  • θ = angle between B and v

Circular Motion​

Magnetic force provides centripetal force:

Bqv=mv2rBqv = \frac{mv^2}{r}

r=mvBqr = \frac{mv}{Bq}

Radius depends on:

  • Mass: Heavier → larger radius
  • Velocity: Faster → larger radius
  • B-field: Stronger → smaller radius
  • Charge: Larger → smaller radius

Electromagnetic Induction​

Faraday's Law

ε=−NΔΦΔtε = -N\frac{\Delta Φ}{Δt}

Where:

  • ε = induced e.m.f.
  • N = number of turns
  • Φ = magnetic flux
  • ΔΦ/Δt = rate of flux change

Magnetic Flux​

Φ=BAcos⁡θΦ = BA\cos θ

Where:

  • B = magnetic flux density
  • A = area
  • θ = angle between B and area normal

Causes of Induced E.m.f.​

  1. Change in B: Stronger or weaker field
  2. Change in area: Larger or smaller loop
  3. Change in angle: Rotating coil or moving magnet
  4. Motion: Moving wire through field

Lenz's Law​

Induced current opposes the change causing it

ε=−NΔΦΔtε = -N\frac{\Delta Φ}{Δt}

Negative sign indicates opposition

Applications​

Generator: Motional e.m.f. when coil rotates in B-field Motor: Magnetic force on current-carrying coil in B-field Transformer: Changing flux induces voltage in secondary coil

AC Generators​

Rotating coil in magnetic field generates alternating e.m.f.

ε=ε0sin⁡(ωt)ε = ε_0\sin(ωt)

Where:

  • ε₀ = peak e.m.f.
  • ω = angular frequency
  • ε₀ = NBAω (maximum when coil perpendicular to field)

Graph​

Sine wave:

  • Peak values: ±ε₀
  • Period: T = 2π/ω
  • Frequency: f = ω/2π

Transformers​

Transformer - Changes voltage using electromagnetic induction

Principle​

Changing current in primary coil:

  • Creates changing magnetic field
  • Induces voltage in secondary coil

Transformer Equation​

VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}

Where:

  • V_p = primary voltage
  • V_s = secondary voltage
  • N_p = primary turns
  • N_s = secondary turns

Step-up transformer: Ns>NpN_s > N_p, Vs>VpV_s > V_p Step-down transformer: Ns<NpN_s < N_p, Vs<VpV_s < V_p

Power Relationship​

Ideal transformer (no losses): Pp=PsP_p = P_s VpIp=VsIsV_pI_p = V_sI_s

Current relationship: IsIp=NpNs\frac{I_s}{I_p} = \frac{N_p}{N_s}

High voltage → low current Low voltage → high current

Alternating Current​

A.C. - Current changes direction periodically

I=I0sin⁡(ωt)I = I_0\sin(ωt)

Where:

  • I₀ = peak current
  • ω = angular frequency

RMS Values​

Root Mean Square - Effective value

Irms=I02≈0.707I0I_{\text{rms}} = \frac{I_0}{\sqrt{2}} ≈ 0.707I_0

Vrms=V02V_{\text{rms}} = \frac{V_0}{\sqrt{2}}

Power with A.C.: P=IrmsVrmsP = I_{\text{rms}}V_{\text{rms}}

(Uses RMS values, not peak)

Frequency​

UK: 50 Hz US: 60 Hz Period: T = 1/f = 20 ms (UK)

AC in Different Components​

Resistor​

Always carries current:

  • Voltage and current in phase
  • P=Irms2RP = I_{\text{rms}}^2R

Inductor (Coil)​

Opposes change in current:

  • Current lags voltage by 90°
  • Inductive reactance: XL=ωLX_L = ωL
  • Power: P=0P = 0 (ideal)

Capacitor​

Opposes change in voltage:

  • Current leads voltage by 90°
  • Capacitive reactance: XC=1ωCX_C = \frac{1}{ωC}
  • Power: P=0P = 0 (ideal)

Solenoid and Electromagnet​

Solenoid - Coil of wire

Magnetic field: B=μ0NILB = μ_0\frac{NI}{L}

Where:

  • μ₀ = permeability of free space
  • N = number of turns
  • I = current
  • L = length

Applications:

  • Electromagnets
  • Relays
  • Motors
  • Inductors

Key Points​

  1. Magnetic force perpendicular to field and current
  2. Induced e.m.f. from changing magnetic flux
  3. Lenz's law: Induced effect opposes change
  4. Transformer equation: V_s/V_p = N_s/N_p
  5. Ideal transformer: Power in = Power out
  6. A.C. has RMS and peak values
  7. RMS = peak/√2 for sine waves
  8. Generators produce A.C. from rotating coil
  9. Solenoid field strength ∝ NI/L
  10. Induction used in transformers, motors, generators

Practice Questions​

  1. Calculate magnetic force
  2. Find radius in magnetic field
  3. Apply Faraday's law
  4. Use Lenz's law
  5. Determine induced e.m.f.
  6. Calculate transformer ratios
  7. Find secondary voltage/current
  8. Calculate power with A.C.
  9. Analyze A.C. circuits
  10. Solenoid field calculations

Revision Tips​

  • Use Fleming's rules correctly
  • Understand Lenz's law concept
  • Know transformer equations
  • Use RMS values for A.C. power
  • Distinguish peak and RMS
  • Understand induction principle
  • Know generator/motor operation
  • Draw field line diagrams
  • Visualize motion effects