A coil of 43 turns in the shape of a rectangle with width 5 cm and length 10 cm is dropped from a position where magnetic field is 0 T to a position where the field is 0.5 T and is directed perpendicular to the plane of the coil. The displacement occurs in a time of 0.431 s. Calculate the resulting average emf induced in the coil

Given that,

Number of turns

N = 43 turns

Dimensions of rectangle

Length L = 10cm = 0.1m

Width W = 5cm = 0.05

Then, area of rectangle

A = L*W = 0.1 * 0.05 = 0.005m²

Initial magnetic field

Bi = 0T

Final magnetic field

Bf = 0.5T

The displacement time

∆t = 0.431s

Induce emf ε?

EMF is given as

ε = - NdΦ/dt

Where magnetic flux

Φ = BA

Note A is constant

Then,

ε = - NdΦ/dt = - Nd (BA) / dt

ε = - N•A•dB/dt

ε = - N•A• (∆B/∆t)

ε = - N•A• (Bf - Bi) / (∆t)

ε = - 43 * 0.005 * (0.5 - 0) / 0.431

ε = - 43 * 0.005 * 0.5 / 0.431

ε = - 0.249 V

The average induced EMF is 0.249V