Question

A circular loop of flexible iron wire has an initial circumference of 165.0cm, but its circumference is decreasing at a constant rate of 12.0cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop of magnitude 0.500T.
A) Find the emf induced in the loop, at the instant when 9.0s have passed,
B) Find the direction of the induced current in the loop, as viewed looking along the direction of the magnetic field inside the loop.

Answer 1

Answer:

Induced emf is 0.0492 volts and it is in clockwise direction.

Explanation:

It is given that,

Initial circumference of a circular loop, C = 165 cm = 1.65 m

Radius, r = 0.825 m

Time, t = 9 s

(A) The circumference is decreasing at a constant rate of 12 cm/s due to a tangential pull on the wire.

$\dfrac{dC}{dt}=-0.12\ m/s$

$\dfrac{d(2\pi r)}{dt}=-0.12\ m/s$

$\dfrac{dr}{dt}=0.019\ m/s$

The induced emf is given by :

$\epsilon=-\dfrac{d(BA)}{dt}$

$\epsilon=2\pi Br\dfrac{dr}{dt}$

$\epsilon=2\pi \times 0.5\times 0.825\times 0.019$

$\epsilon=0.0492\ volts$

(B) the direction of induced emf is clockwise as viewed looking along the direction of the magnetic field inside the loop.

Hence, this is the required solution.