Question

A non-uniform magnetic field is pointing into the paper, as shown in the diagram below. The magnetic field is. stronger on the top and gradually becomes weaker on the bottom. A metal loop locates in the middle of the field, shown as the solid square in the graph. If the loop is rotating counter-clockwise around a corner into the position indicated by the dash line. Please carefully answer the following questions with your reasons. (a) Is there any induced current in the loop? (b) If the answer is yes in previous question, what's the direction of the induced current? If not, why not? (c) If the loop continues to rotate in the same direction for another 90 degrees, from the dashed position. Please draw what the new location of the loop in the "after" graph. (d) Is there any induced current in step c? if so, what's its direction? If not, why not? XXX XX ХХХХХХ xx xxxxxxxxxx ХХХХХХХХХ xx xxx xxx Rotation XX xxx ХХХХ xxx xxx xxxxxxx Х Xxx Rotation XX х х ХХХХ xx ху XX ---- xxxx XX xx XX Before After

Answer 1

Lenz's law states that the direction of induced current in a loop is such that it opposes the change in magnetic flux through it.

Consider a situation, there is a loop placed in a region of magnetic field that is pointed into the plane of loop when viewed.

The following observations can be noted:

1. If somehow, the magnetic field through the loop decreases due to which magnetic flux decreases, then the direction of current induced in the loop will be clockwise.
2. If somehow, the magnetic field through the loop increases due to which magnetic flux also increases, then the direction of current induced in the loop will be counter-clockwise

Now, in our problem, the magnetic field directed into the plane of figure.

When the loop rotates counter-clockwise, it moves from high strength magnetic field to low strength magnetic field.

a) As there is change of magnetic field through the loop, there is change in magnetic flux. Also, we can say due to decrease in magnetic field through the loop the magnetic flux is decreased.

Therefore, current is induced in the loop. [answer]

b) From the point '1' given in the observations above, we can say the direction of induced current is clockwise. [answer]

c) Now, the loop further rotates by 90 degree, this time the loop moves from low strength magnetic field to high strength magnetic field.

see the diagram:

x xxxxx xx x т к x x x x x, xx XX XX XX х x x x x x x х X x X x х X x

d) As there is change of magnetic field through the loop, there is change in magnetic flux. Also, we can say due to increase in magnetic field through the loop the magnetic flux is increased.

Therefore, current is induced in the loop. [answer]

From the point '2' given in the observations above, we can say the direction of induced current is counter-clockwise. [answer]