Magnetic Fields (Copy)

A2 Level Physics – Section 20: Magnetic Fields & Electromagnetic Induction (Detailed Notes)

20.1 Concept of a Magnetic Field

1. Definition

• A magnetic field is a region where a force acts on a moving charge or magnetic material.
• Produced by:
  • Moving charges (e.g. current in wires)
  • Permanent magnets

2. Magnetic Field Lines

• Show the direction of force on a North pole.
• Lines go from North to South outside the magnet.
• Closer lines = stronger field.

20.2 Force on a Current-Carrying Conductor

1. Magnetic Force on a Current-Carrying Wire

• A current-carrying wire in a magnetic field experiences a force.

Equation:
F = BIL·sinθ

• F = force (N)
• B = magnetic flux density (T)
• I = current (A)
• L = length of wire (m)
• θ = angle between wire and magnetic field

2. Fleming’s Left-Hand Rule

• Thumb = Force (Motion)
• First finger = Field (B)
• Second finger = Current (I)

3. Magnetic Flux Density Definition

• B = F / (I·L)
  • When wire is perpendicular to B (sinθ = 1)
• Unit: tesla (T)
• 1 T = 1 N/(A·m)

20.3 Force on a Moving Charge

1. Force on a Charge

• Moving charges also experience magnetic force:

F = B·q·v·sinθ

• q = charge (C)
• v = speed (m/s)
• θ = angle between velocity and B

2. Direction of Force

• Use Fleming’s left-hand rule (replace current with direction of positive charge motion)

3. Hall Effect

• Charge carriers deflected in magnetic field → Hall voltage (Vᴴ) across conductor

Vᴴ = B·I / (n·t·q)

• B = magnetic field strength (T)
• I = current (A)
• n = charge carrier density (m⁻³)
• t = thickness (m)
• q = charge (C)

4. Hall Probe

• Uses the Hall voltage to measure magnetic flux density
• Sensitive, used in lab experiments and devices

5. Motion in Uniform Magnetic Field

• Charged particle moves in a circular path when velocity is perpendicular to B
• Centripetal force = magnetic force:
  mv² / r = Bqv
  → r = mv / (Bq)

6. Velocity Selector

• Combines electric field (E) and magnetic field (B):
  • Fields adjusted so that only particles with speed v = E / B pass undeflected

20.4 Magnetic Fields Due to Currents

1. Field Patterns

• Long straight wire: concentric circles around wire (use right-hand grip rule)
• Flat circular coil: similar to bar magnet at center
• Solenoid: uniform field inside, bar magnet shape outside

2. Ferrous Core in Solenoid

• Inserting a ferromagnetic core (e.g. iron) into solenoid increases the magnetic field strength

3. Forces Between Parallel Currents

• Two parallel current-carrying conductors exert forces on each other due to their magnetic fields:
  • Same direction currents → attract
  • Opposite direction currents → repel
• Direction: Use right-hand rule for each wire’s field and determine interaction

20.5 Electromagnetic Induction

1. Magnetic Flux (Φ)

• Φ = B·A·cosθ
  • B = magnetic flux density (T)
  • A = area perpendicular to B (m²)
  • θ = angle between B and normal to surface
• Unit: weber (Wb)

2. Magnetic Flux Linkage

• Flux linkage = N·Φ
  • N = number of turns in coil
  • Φ = flux through one loop

3. Faraday’s Law of Induction

• Induced e.m.f. ∝ rate of change of magnetic flux linkage

E = –d(NΦ) / dt

• Faster change = greater e.m.f.
• E = induced e.m.f. (V)

4. Lenz’s Law

• Induced e.m.f. is always in a direction to oppose the change causing it
• Negative sign in Faraday’s law represents Lenz’s law
• Ensures conservation of energy

5. Factors Affecting Induced e.m.f.

• Number of turns (N)
• Area of coil (A)
• Magnetic field strength (B)
• Angle θ
• Speed of relative motion

Demonstration Experiments:

• Moving magnet through coil
• Moving coil in magnetic field
• Rotating a coil in a uniform B field (generator principle)