Question

If coil is placed perpendicular to field lines then number of lines passing through coil are :

• A. minimum
• B. maximum
• C. zero
• D. may be max. or min.

Answer 1

The correct option is B maximum

The magnitude of the induced emf in a circuit is proportional to the time rate of magnetic flux linked with the circuit.

Consider a rectangular loop which rotates in a uniform magnetic field, around an axis in the plane of the loop and passing through the centres of opposite sides.

If the area of the loop is A and the field strength is B and the normal to the loop makes an angle phi with the field direction at any instant, the flux through the loop at any time is B A cos phi. The flux is a maximum when the loop is normal to the field $(\varphi =0)$ and zero when the loop is aligned parallel to the field $(\varphi =90).$

If the loop rotates with angular velocity w, then we can substitute phi = wt, and we can then write flux at any instant $=ABcoswt.$

The induced emf is $E=\frac{-d\left(ABcoswt\right)}{dt}$

$E=ABwsinwt.$

The answer to your question follows from that last expression. The induced emf is a sinusoidal function. It will be a minimum (that is zero), when phi = wt = 0, when the plane of the coil is normal to the field, and it will be maximum when $\varphi =wt=90$, or when the plane of the loop is parallel to the field