Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

An EMF is induced in a loop if the magnetic field is changing, and also if the m

ID: 1499827 • Letter: A

Question

An EMF is induced in a loop if the magnetic field is changing, and also if the magnetic field "seen" by the loop is changing. Consider a circular loop of flexible iron wire which has an initial radius of 82.0 cm , but the radius is decreasing at the rate 15.0 cm/s . The loop is in a constant uniform magnetic field of magnitude 0.600 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.

Part A.) Find the magnitude of the emf E induced in the loop after exactly time   5.00 s    has passed since the radius of the loop started to decrease.

Part B.) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field. (Clockwise or counterclockwise)

Explanation / Answer

Here,

radius , r = 82 cm = 0.82 m

dr/dt = 15 cm = 0.15 m/s

magnetic field , B = 0.6 T

part A)

at time , t = 5 s

radius , r = 0.82 - 0.15 * 5

r = 0.07 m

dA/dt = 2pi * r * dr/dt

magnitude of emf E = dA/dt * magnetic field

magnitude of emf E = 2pi * 0.07 * 0.15 * 0.6

magnitude of emf E = 0.5654 V

the magnitude of the emf E in the loop is 0.5654 V

part B)

as the magnetic flux is decreasing through the loop

the direction of induced magnetic field will be same as the applied field

Using right hand rule

the direction of induced current will be Counterclockwise