Question

A rectangular loop of sides 8 cm and 2 cm with a small cut is stationary in a uniform magnetic field directed normal to the loop. The magnetic field is reduced from its initial value of 0.3 T at the rate of 0.02 T s^-1 If the cut is joined and loop has a resistance of 1.6 Ω, then how much power is dissipated by the loop as heat?

Options

• 6.2 × 10^-10 W

• 6.1 × 10^-10 W

• 6.3 × 10^-10 W

• 6.4 × 10^-10 W

Answer 1

6.4 × 10^-10 W

Explanation:

A = 8 × 2 = 16 sq cm = 16 × 10^-4 m^-2 

`"dB"/"dt" = - 0.02 " Ts"^-1`

∴ Induced emf e = `- ("d"phi)/"dt" = "AdB"/"dt"`

`= - 16 xx 10^-4 (- 0.02) = 32 xx 10^-6 "V"`

Power loss = `"e"^2/"R" => (32 xx 10^-6)^2/1.6`

P = `(32 xx 10^-6 xx 32 xx 10^-6)/1.6`

P = 64 × 10^-11

P = 6.4 × 10^-10 W