Question

A circular coil of radius 10 cm and 25 turns is rotated about its vertical diameter with an angular speed of 40 rad S^-1, in a uniform horizontal magnetic field of magnitude 5?10^-2T. Calculate the emf induces in the coil. Also find the current in the coil if the resistance of the coil is 15 ohm.

Answer 1

Dear student,

Radius of the circular coil, r = 10 cm = 0.1 m
Area of the coil, A = πr² = π × (0.1)² m²
Number of turns on the coil, N = 25
Angular speed, ω = 40 rad/s
Magnetic field strength, B = 5 × 10⁻² T
Resistance of the loop, R = 15 Ω
Maximum induced emf is given as:
$$\begin{gathered} e=N\omega AB \\ e=25\times 40\times \pi \times (0.1{)}^2\times 5\times {10}^{-2} \\ e=1.5V \end{gathered}$$

The maximum emf induced in the coil is 1.5 V. Over a full cycle, the average emf induced in the coil is zero. Maximum current is given as:
$I=\frac{e}{R}=\frac{1.5}{15}=0.1A$

Regards