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 maximum emf induced in the coil. Also find the current in the coil if the resistance of the coil is 15Ω.

Answer 1

Emf induced in the coil = ε = nAB sin (ωt); 

Area = πr² Substitution 

E = (25 × 3.14 × 10 × 10^-2 × 10^-2 × 5 × 10^-2 × 40) sin(40t)

E = (25 × 3.14 × 10 × 10^-2 × 10 × 10^-2 × 5 × 10² × 40) sin (40t) 

Induced emf ε_inst = 1.57 sin (40 t) 

V or ε = 1.57 V

\(I=\frac{\varepsilon}{R}\)

Current I_max = 0.1047 sin40t A or I_max = 0.1047A

(Note: since it is not mentioned either instantaneous or maximum or average value of induced emf in the question, if a student calculates by mentioning any of the above values marks can be awarded, also for the other values of θ = ωt)