Question

A circular loop 40 cm in diameter is made froma flexible conductor and lies at right angles to a uniform 12-T magnetic field. At time t = 0 the loop starts to expand, its radius increasing at the rate of 5.0 mm/s Find the induced emf in the loop: a) at t 1.0 s and b) at t 10 s.

Answer 1

Step-by-step explanation:

As we know that magnetic flux is given by

`\phi = B.A`

`\phi = B.\pi r^2`

now from Faraday's law

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

`EMF = (d(B. \pi r^2))/(dt)`

`EMF = 2\pi r B (dr)/(dt)`

now we have

`r = 40/2 = 20 cm`

B = 12 T

`(dr)/(dt) = 5 * 10^(-3) m/s`

Part a)

now at t = 1 s

r = 20 + 0.5 = 20.5 cm

`EMF = (2\pi (0.205))(12)(5 * 10^(-3))`

`EMF = 0.077 Volts`

Part b)

now at t = 10 s

r = 20 + 0.5(10) = 25 cm

`EMF = (2\pi (0.25))(12)(5 * 10^(-3))`

`EMF = 0.094 Volts`