Question

A metal rod is forced to move with constant velocity along two parallel metal rails, connected with a strip of metal at one end across a magnetic field (B) of 0.5 T, pointing out of the page. The rod is of length 45 cm and the speed of the rod is 70 cm/s. The rod has a resistance of 10 Ω and the resistance of the rails and connector is negligible. What is the rate at which energy is being transferred to thermal energy?

(a) 0.225 W

(b) 22.55 W

(c) 2.25 × 10^-4 W

(d) 2.25 × 10^-3 W

This question was addressed to me in homework.

Origin of the question is Electromagnetic Induction in section Electromagnetic Induction of Physics – Class 12

Answer 1

Right choice is (d) 2.25 × 10^-3 W

Easy explanation: Given: B = 0.5 T; v = 70 cm/s = 70 × 10^-2 m/s; L = 45 cm = 45 × 10^-2 m; R = 10 Ω

Motional emf (E) = vLB = 70 × 10^-2 × 45 × 10^-2 × 0.5

E = 0.15 V

Current (I) = \(\frac {E}{R}\)

I = \(\frac {0.15}{10}\)

I = 0.015 A

Rate of energy or power (P) = I^2R

P = 0.015^2 × 10

P = 2.25 × 10^-3 W

Therefore, the rate of energy transfer is 2.25 × 10^-3 W.