Question

Explain the rate of change of magnetic flux due to change in the orientation of the loop.

Answer 1

Faraday's Law of Electromagnetic Induction:

Faraday performed a series of experiments with a closed circuit and varying magnetic field and observed the following points:

1. When the magnetic flux linked with the circuit changes with time a current is induced in the circuit.
2. The direction of the induced current is reversed if the magnetic field begins to decay instead of growing with time.
3. The magnitude of induced emf is proportional to the rate of change of the magnetic field.

Derivation of Magnetic Flux:

Suppose we consider a vertical loop of wire rotating with angular velocity $\omega$ in a uniform steady magnetic field $\overrightarrow{B}$ acting in the horizontal direction.

If at any time $t$ the normal $\left(\hat{n}\right)$ to the plane of the coil makes an angle $\theta =\omega t$ with $\overrightarrow{B}$ the flux linked with the coil of area $S$ at the instant $t$ would be,

$\varphi =\overrightarrow{B}.\hat{n}S$

$=BS\cos \omega t$

According to Faraday's law of induction,

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

This principle is used in earth inductors for the measurement of the earth's horizontal magnetic field and the angle of dip.