Question

A flat loop of wire consisting of a single turn of cross-sectional area 7.30 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.00 T in 0.93 s. What is the resulting induced current if the loop has a resistance of 1.30 ?

Answer 1

As per Faraday's law of induction the EMF induced in the loop is due to rate of change in magnetic flux linked with the loop

So here we can say

`EMF = (d\phi)/(dt)`

`EMF = A(dB)/(dt)`

`EMF = A(B_1 - B_2)/(\Delta t)`

Given that

`B_1 = 0.500 T`

`B_2 = 0.200 T`

`\Delta t = 0.93 s`

`A = 7.30 cm^2`

now plug in all values in it

`EMF = 7.30* 10^(-4) ((0.500 - 0.200)/(0.93))`

`EMF = 2.35 * 10^(-4) Volts`

now in order to find induced current we can use Ohm's law

`V = iR`

`2.35 * 10^(-4) = i (1.30)`

`i = 1.81 * 10^(-4) A`