Electric and Magnetic Fields and Electromagnetic Induction

Electric fields

An electric field is a region where a charge feels a force. Field lines go from positive to negative.

Coulomb's law (force between point charges):

F = Qq ÷ (4πε₀r²)

(ε₀ = permittivity of free space). Like gravitational fields, it's an inverse-square law, but can be attractive or repulsive.

• Electric field strength: E = F/Q; for a radial field E = Q/(4πε₀r²); for a uniform field between parallel plates E = V/d (V/m).
• Electric potential: V = Q/(4πε₀r) — positive for a positive charge (unlike gravity).

A charged particle in a uniform field (e.g. between plates) experiences a constant force F = EQ, moving in a parabolic path — similar to projectile motion.

Comparison with gravitational fields

Both are inverse-square. Key difference: gravity is always attractive; electric forces can attract or repel, and are far stronger.

Magnetic fields

A magnetic field exerts a force on a moving charge or a current-carrying wire.

• Force on a current-carrying wire: F = BIL sin θ (B = magnetic flux density in tesla, θ = angle between wire and field). Maximum when the wire is perpendicular to the field.
• Force on a moving charge: F = BQv. This force is always perpendicular to the velocity, so charged particles move in circles (the basis of cyclotrons/mass spectrometers).
• Fleming's left-hand rule gives the direction of the force (thumb = force, first finger = field, second finger = current).

Electromagnetic induction

A changing magnetic field induces an EMF:

• Magnetic flux: Φ = BA (weber); flux linkage = NΦ (N turns).
• Faraday's law: the induced EMF is proportional to the rate of change of flux linkage: ε = −N(ΔΦ/Δt).
• Lenz's law: the induced current opposes the change that caused it (hence the minus sign — conservation of energy).

Applications: generators (rotating coil in a field produces alternating EMF) and transformers (change AC voltage; Vs/Vp = Ns/Np).

Worked example

A wire of length 0.20 m carrying 3.0 A sits perpendicular to a 0.50 T field. Find the force on it.

• F = BIL = 0.50 × 3.0 × 0.20 = 0.30 N. ✓

Common mistakes

• Forgetting electric fields can be repulsive as well as attractive (unlike gravity).
• Omitting sin θ in F = BIL sin θ.
• Missing the minus sign / Lenz's law when explaining induced current direction.

Exam tips

• Compare electric and gravitational fields (both inverse-square; electric can repel).
• Use F = BIL and F = BQv; apply Fleming's left-hand rule.
• State Faraday's (rate of flux change) and Lenz's (opposes change) laws for induction.

Key facts to remember

• Electric field: Coulomb's law F = Qq/(4πε₀r²); E = V/d for uniform fields; can attract or repel.
• Magnetic force: F = BIL sin θ (wire), F = BQv (moving charge, circular motion); Fleming's left hand.
• Induction: flux Φ = BA; Faraday (ε = −N ΔΦ/Δt) and Lenz (opposes change) → generators/transformers.