A-Level Magnetic flux, the induction laws of Faraday and Lenz, and power transformers: worked solution

Question

Coupled to a vehicle's wheels, a massive aluminium disc 0.72 m across spins in a 0.017 T field normal to its face, its radial spoke OP sweeping the field. Obtain the flux this spoke sweeps per turn, and give the unit. [3]

Principle: the magnetic flux through a flat area A that lies perpendicular to a uniform magnetic field is Φ = BA, where B is the magnetic flux density in tesla (T) and A is the area in m². Step 1 - find the radius. The spoke OP runs from the centre O of the disc out to a point P on the rim, so its length is the radius. The disc is 0.72 m across, and the diameter is twice the radius, so r = d/2 = 0.72 m / 2 = 0.36 m. Step 2 - find the area swept in one turn. As the spoke makes one complete revolution its far end traces the rim and the spoke sweeps over the whole face of the disc once. That area is the area of a circle of radius r: A = πr² A = π × (0.36 m)² A = π × 0.1296 m² A = 0.4072 m². Step 3 - apply the flux equation. The field is stated to be normal (perpendicular) to the face of the disc, so it is already perpendicular to the swept area and no cos θ factor is needed. Φ = B × A Φ = 0.017 T × 0.4072 m² Φ = 6.92 × 10⁻³ T m². Step 4 - the unit. One tesla metre squared is defined as one weber, 1 T m² = 1 Wb. So the flux swept per turn is Φ ≈ 6.9 × 10⁻³ Wb (weber), to 2 significant figures.