Question

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

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

Answer 1

Answer: (B), (C)

The magnetic field is in the same plane as the circular coil and it may or may not vary
The magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably

When a circular coil expands radially in a region of magnetic field, induced mf developed is

$\epsilon =\frac{d\varphi }{dt}=\frac{d(B\cdot A)}{dt}$

case-1:

When circular coil expands radially in a region of magnetic field such that the magnetic field is in the same plane as the circular coil or we can say that direction of magnetic field is perpendicular to the direction of area (increasing) so that their dot product is always zero and hence change in magnetic flux is also zero.

So $\epsilon =0$,

Case-2:

The magnetic field has a perpendicular (to the plane of the coil) component whose-magnitude is decreasing suitably in such a way that the dot product of magnetic field and surface area of plane of coil remain constant at every instant.

$\epsilon =\frac{d\varphi }{dt}=0$