Question

Write Faraday's laws of electromagnetic induction and obtain an expression of induced e.m.f.

Answer 1

Faraday's law of electromagnetic induction:
(i) Whenever there is a change in magnetic flux linked with a closed coil, an induced e.m.f. produced and current flows through the coil. This induced e.m.f. remains till the flux changes.
(ii) The induced e.m.f. is directly proportional to the rate of change of flux.
Expression for induced e.m.f.: Let at any instant, the flux linked with a circuit changes from ${\Phi }_1$ to $\Phi$ in t second.
$\therefore$ Rate of change of flux $=\frac{{\Phi }_2-{\Phi }_1}{t}$
or Induced e.m.f., $e\propto -\frac{{\Phi }_2-{\Phi }_1}{t}$
or $e=-K\frac{{\Phi }_2-{\Phi }_1}{t}$
Where, K is a constant, its value is S.I. system is $1$.
$\therefore e=-\left(\frac{{\Phi }_2-{\Phi }_1}{t}\right)$
or $e=-\frac{d\Phi }{dt}$
The negative sign shows that induced e.m.f. opposes the change of flux.