Question

A circular loop of flexible iron wire has an initial circumference of 167 cm, but its circumference is decreasing at a constant rate of 15.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 T, which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.A) Find the magnitude of the emf E induced in the loop after exactly 8.00 s has passed since the circumference of the loop started to decrease.B) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field. (Clockwise or Counterclockwise?)

Answer 1

Answer:

Part a)

$EMF = 5.6 \times 10^{-3} V$

Part b)

Since the radius is decreasing so induced current will increase the flux through the coil

So it would be clockwise in direction

Explanation:

As we know that magnetic flux linked with the coil is given as

$\phi = \pi r^2 B$

now the rate of change in flux is given as

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

now we know that circumference is decreasing at rate of 15 cm/s

so here we know the length of circumference as

$C = 2\pi r$

So rate of change in circumference is

$\frac{dC}{dt} = 2\pi \frac{dr}{dt}$

$\frac{1}{2\pi}(15 cm) = \frac{dr}{dt}$

final length of circumference at t = 8 s

$C = 167 - (15)(8) = 47$

Part a)

Now the induced EMF is given as

$EMF = (2\pi r)(\frac{1}{2\pi})(0.15)(0.5)$

$EMF = (0.47)(\frac{1}{2\pi})(0.15)(0.5)$

$EMF = 5.6 \times 10^{-3} V$

Part b)

Since the radius is decreasing so induced current will increase the flux through the coil

So it would be clockwise in direction