The drawing shows that a uniform magnetic field is directed perpendicularly out

Question

The drawing shows that a uniform magnetic field is directed perpendicularly out of the plane of the paper and fills the entire region to the right of the y-axis. There is no magnetic field to the left of the y-axis. A rigid semicircular loop is made of copper wire. Its original orientation is shown. The semicircle rotates clockwise about the origin. What is the direction (clockwise or counterclockwise) of the induced current when the semicircle is crossing (a) the +y axis, (b) the +x axis, (c) the -y axis, and (d) the -x axis? For each case, justify your answer by stating how the flux changes and the direction of the induced magnetic field.

Explanation / Answer

A.      When the loop crosses the +ve y-axis ,there is increase in the magnatic flux in the loop. So, there is a induced current in the loop.

According to Lenz law , the induced current try to decrease magnetic flux which is causing it, So it produce a magnetic field which has a direction opposite to the direction of given field. According to right hand curl rule , induced current must be clockwise.

B.      As per discussion in part A , there is also increase in flux through loop when it crossing the +ve x-axis .So, there is a induced current which try to decrease the net magnetic flux through the loop.

so, Induced current must be clock wise .

C.   When loop crossing the -ve y-axis, there is decrease in magnetic flux through the loop. so, induced current try to increase the magnetic flux through the loop.

Induced current must be anticlock wise..

D. When loop crossing the -ve x-axis, there is decrease in magnetic flux through the loop. So, induced current try to increase the magnetic flux through the loop.

Induced current must be anticlock wise.

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