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

Answer:

Explanation:

As we know that magnetic flux is given by

$\phi = B.A$

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

now from Faraday's law

$EMF = \frac{d\phi}{dt}$

$EMF = \frac{d(B. \pi r^2)}{dt}$

$EMF = 2\pi r B \frac{dr}{dt}$

now we have

$r = 40/2 = 20 cm$

B = 12 T

$\frac{dr}{dt} = 5 \times 10^{-3} m/s$

Part a)

now at t = 1 s

r = 20 + 0.5 = 20.5 cm

$EMF = (2\pi (0.205))(12)(5 \times 10^{-3})$

$EMF = 0.077 Volts$

Part b)

now at t = 10 s

r = 20 + 0.5(10) = 25 cm

$EMF = (2\pi (0.25))(12)(5 \times 10^{-3})$

$EMF = 0.094 Volts$