Question

The plane of a conducting loop is oriented parallel to the x-y plane. A magnetic field is directed in the -z direction.

Which one of the following actions will not change the magnetic flux through the loop?

A) Decrease the area of the loop.

B) Decrease the strength of the magnetic field.

C) Increase the strength of the magnetic field.

D) Rotate the loop about an axis that is directed in the z direction and that passes through the center of the loop.

E) Rotate the loop about an axis that is directed in the y direction and that passes through the center of the loop.

Answer 1

Answer:

D) Rotate the loop about an axis that is directed in the z direction and that passes through the center of the loop

Explanation:

The magnetic flux is defined as the total magnetic field times the area normal to the magnetic field lines.

Mathematically:

$\phi_B=\vec{B}.\vec{A}$

where:

$\vec{A}=$ area vector directed normal to the surface

$\vec{B}=$ magnetic field vector

• Now as the area of the loop changes there will be a change in magnetic flux.

• Change in the magnetic field strength will also change the flux accordingly.
• Since the loop lies in the x-y plane we will get a different area of normal projection on the plane whenever the inclination of the loop changes in xy-plane.
• Since the area of the loop all remains in the magnetic field while it rotates about the z axis to its center hence this will not affect area subjected  to the magnetic field.