A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because

Options

A. the magnetic field is constant.
B. the magnetic field is in the same plane as the circular coil and it may or inay not vary.
C. the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
D. there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

Answer

B, C

Explanation

The flux linked with a coil in a uniform magnetic field is given by
`phi = BA costheta`
where `theta` is the angle between area vector (normal to the plane) and magnetic field. As in option (b), when the magnetic field is in plane of the coil, then `90 ^(@)` .
`:. phi= 0`
Even if the magnetic field varies, the flux linked with the coil remains unchanged (remains zero) and no emf will be induced in this case . Hence, option (b) is correct.
Now as per option (c), when the coil is expanding, the flux linked with the coil should increase when the magnetic field is constant but in case of magnetic field having a component in the direction perpendicular to the plane of coil (parallel to area vector) and decreasing in such a way that magnetic flux linked with the radially expanding coil remains constant. In this case, no emf is induced in the coil.
Options (b) and (c) are correct.
In options (a) and (d) flux will certainly change hence these options cannot be correct.