The magnitude of the induced e.m.f is directly proportional to the rate of change of magnetic flux linkage
A small rectangular coil contains 350 turns of wire. The longer sides are 3.5 cm and the shorter sides are 1.4 cm.
The coil is held between the poles of a large magnet so that the coil can rotate about an axis through its centre. The magnet produces a uniform magnetic field of flux density 80 mT between its poles. The coil is positioned horizontally and then turned through an angle of 40° in a time of 0.18 s.
Calculate the magnitude of the average e.m.f induced in the coil.
Step 1: Write down the known quantities
Step 2: Write out the equation for Faraday’s law:
Step 3: Write out the equation for the change in flux linkage:
Δ(NΦ) = NA(ΔB)
Step 4: Determine the change in magnetic flux linkage
Δ(NΦ) = NA(ΔB) = 350 × (4.9 × 10-4) × (80 × 10-3) = 0.014 Wb turns
Step 5: Substitute change in flux linkage and time into Faraday’s law equation:
The 'magnitude' of the e.m.f just means its size, rather than direction. This is often what is required in exam questions, so the minus sign in Lenz's law is often not needed in calculations.
However, you may be expected to explain the significance of the minus sign. Be prepared to interpret it as an expression of Lenz's Law. You can find this is described on the next page.