State and explain Faraday's Laws of electromagnetic induction.
On the basis of his experiments, Faraday stated the laws of electromagnetic induction as given below :
(i) Faraday's First Law of Electromagnetic Induction (Qualitative Law) :
Whenever magnetic flux linked with a closed conductor (or coil) changes, an e.m.f. is induced in it.
This induced e.m.f. lasts so long as the change in magnetic flux continues in the coil.
(ii) Faraday's Second Law of electromagnetic induction (Quantitative Law) :
The magnitude of the induced e.m.f. in a closed conductor or a coil is directly proportional to the rate of change of magnetic flux linked with the conductor (or coil).
Expression for Induced e.m.f.
Let $\phi_1$ be magnetic flux linked with a closed circuit or coil at time $t_1$ and $\phi_2$ be magnetic flux linked with a closed circuit or coil at time $t_2$.
Then change in magnetic flux in the time interval $(t_2 - t_1) = (\phi_2 - \phi_1)$
Induced e.m.f.
$\varepsilon \propto \frac{(\phi_2 - \phi_1)}{(t_2 - t_1)}$
$\varepsilon = -k \frac{(\phi_2 - \phi_1)}{(t_2 - t_1)}$
where $k$ is constant of proportionality. In SI, $k = 1$
$\varepsilon = - \frac{(\phi_2 - \phi_1)}{(t_2 - t_1)}$
$\varepsilon = - \frac{d\phi_B}{dt} \qquad ...(i)$
Magnitude of induced e.m.f. is given by
$|\varepsilon| = \left| \frac{d\phi_B}{dt} \right| \qquad ...(ii)$
Negative sign in eqn. (i) shows the direction of induced e.m.f. in the closed circuit or a coil.
If a coil has $N$ number of turns, then eqn. (i) can be written as
$\varepsilon = -N \frac{d\phi_B}{dt} \qquad ...(iii)$
If $R$ be the resistance of the closed circuit, then induced current in the closed circuit is given by
$I = \frac{\text{e.m.f. (Induced)}}{\text{Resistance of the circuit}}$
$I= \left| \frac{\varepsilon}{R} \right|$
$I= \frac{d\phi_B}{Rdt} \qquad ...(iv)$
Methods of producing induced e.m.f. :
According to Faraday's law of electromagnetic induction, induced e.m.f. is given by
$\varepsilon = - \frac{d\Phi_B}{dt}$
where
$\Phi_B = BA \cos \theta$
$\therefore \varepsilon = - \frac{d}{dt} (BA \cos \theta)$
Thus, induced e.m.f. in a closed loop or circuit can be produced by changing either the
(i) area (A) of the closed loop or circuit with time,
(ii) magnetic field (B) with time,
(iii) orientation ($\theta$) of the loop with respect to the direction of the magnetic field.