A Level Physics: Magnetic Fields — Revision Notes

Condensed for the final weeks. For the full explanation, use the Magnetic Fields study guide.

Forces

On a current-carrying wire:   F = B I L sin(theta)
On a moving charge:           F = B Q v sin(theta)

theta = angle between the field and the current/velocity
Maximum force when theta = 90 degrees; ZERO when parallel

Defining the tesla: the tesla is the flux density that produces a force of 1 N per metre of conductor carrying 1 A, when the conductor is perpendicular to the field.

Fleming’s left-hand rule (motor effect): First finger = Field, seCond finger = Current, thuMb = Motion.

For a negative charge, current direction is opposite to the velocity — reverse the answer. This catches almost everyone at least once.

Worked example. A wire of length 0.20 m carries a current of 5.0 A perpendicular to a field of flux density 0.30 T.

F = B I L = 0.30 x 5.0 x 0.20 = 0.30 N

If the wire instead ran parallel to the field, θ = 0° and sin θ = 0, so the force would be zero regardless of current or field strength.

Charged particle in a magnetic field

The force is always perpendicular to velocity, so it changes direction but never speed. The particle moves in a circle:

B Q v = m v^2 / r      ->      r = m v / (B Q)

Because the force is perpendicular to motion, no work is done and kinetic energy is constant.

Larger mass or speed → larger radius. Stronger field or greater charge → tighter circle.

Worked example. An electron (Q = 1.6 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m s⁻¹ perpendicular to a field of flux density 0.50 T.

F = B Q v = 0.50 x 1.6x10^-19 x 2.0x10^6 = 1.6x10^-13 N

Magnetic flux and flux linkage

flux            phi = B A cos(theta)          webers (Wb)
flux linkage    N phi = B A N cos(theta)      weber-turns

θ is measured between the field and the normal to the area — not the plane. Flux is maximum when the field is perpendicular to the area, zero when parallel to it — measuring θ from the coil’s plane instead of its normal is a common source of a sign or magnitude error.

Electromagnetic induction

Faraday’s law — the magnitude of the induced e.m.f. equals the rate of change of flux linkage:

E = - d(N phi) / dt

Lenz’s law — the induced e.m.f. opposes the change producing it. That is the minus sign, and it is a statement of conservation of energy: if the induced current helped the change, energy would be created from nothing.

The three ways to induce an e.m.f.

1. Change the field strength B.
2. Change the area A.
3. Change the angle θ (rotation — this is how a generator works).

For a coil rotating at angular frequency ω, the e.m.f. varies sinusoidally with peak value NBAω.

Exam traps

• Forgetting to reverse the direction for a negative charge in Fleming’s left-hand rule.
• Measuring θ from the plane of the coil instead of from the normal.
• Saying a magnetic field does work on a moving charge — it never does; the force is perpendicular to motion.
• Omitting the minus sign in Faraday’s law, or failing to explain it as Lenz’s law.
• Confusing flux (BA) with flux linkage (NBA).
• Using F = BIL when the wire is parallel to the field — the force is then zero.
• Forgetting the tesla is defined per metre of conductor per ampere, not simply “a unit of field strength” with no numerical anchor.

Self-test

1. State Fleming’s left-hand rule and what each digit represents.
2. An electron moves at right angles to a magnetic field. Describe its path and explain why its speed is unchanged.
3. Give the equation for the radius of that path.
4. State Faraday’s and Lenz’s laws.
5. Why does Lenz’s law follow from conservation of energy?
6. Define the tesla in terms of force, current and length.
7. An electron (Q = 1.6 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m s⁻¹ perpendicular to a 0.50 T field. Find the force on it.
8. A wire of length 0.20 m carries 5.0 A perpendicular to a 0.30 T field. Find the force, and state what happens if the wire instead runs parallel to the field.

Answers: 1. First finger = field, second finger = current, thumb = motion (force); all mutually perpendicular. 2. A circle — the force is always perpendicular to the velocity, so it changes direction continuously but does no work, leaving the speed and kinetic energy constant. 3. r = mv/(BQ). 4. Faraday: the induced e.m.f. is proportional to the rate of change of flux linkage. Lenz: the induced e.m.f. acts to oppose the change causing it. 5. If the induced effect reinforced the change, the change would grow without limit and energy would be created from nothing; opposing it means work must be done to sustain the change. 6. The flux density that produces a force of 1 N per metre of conductor carrying 1 A, perpendicular to the field. 7. F = BQv = 0.50 × 1.6×10⁻¹⁹ × 2.0×10⁶ = 1.6×10⁻¹³ N. 8. F = BIL = 0.30 × 5.0 × 0.20 = 0.30 N; parallel to the field, θ = 0° so sin θ = 0 and the force is zero.