Question

A flat coil having 160 turns, each with an area of 0.20 m 2, is placed with the plane of its area perpendicular to a magnetic field of 0.40 T. The magnetic field changes uniformly from 0.40 T in the + x direction to 0.40 T in the - x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil during this change?

Answer 1

10.2 Watt

Step-by-step explanation:

`N` = number of turns in flat coil = 160

`A` = area = 0.20 m²

B₀= initial magnetic field = 0.40 T

`B` = final magnetic field = - 0.40 T

Change in magnetic field is given as

ΔB = B - B₀ = - 0.40 - 0.40 = - 0.80 T

`t` = time taken for the magnetic field to change = 2.0 s

Induced emf is given as

`E = (- N A \Delta B)/(t)`

`E = (- (160) (0.20) (- 0.80))/(2)`

`E` = 12.8 volts

`R` = Resistance of the coil = 16 Ω

Power is given as

`P = (E^(2))/(R)`

`P = ((12.8)^(2))/(16)`

`P` = 10.2 Watt