Faraday's Laws of Electromagnetic Induction
Category : JEE Main & Advanced
(1) First law : Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is change or cutting of flux.
(2) Second law : The induced emf is given by rate of change of magnetic flux linked with the circuit i.e. \[e=-\frac{d\varphi }{dt}\]. For N turns \[e=-\frac{N\,d\varphi }{dt}\] ; Negative sign indicates that induced emf (e) opposes the change of flux.
(3) Other formulae : \[\phi =BA\,\cos \theta ;\] ; Hence \[\phi \] will change if either, B, A or \[\theta \] will change
So \[e=-N\frac{d\varphi }{dt}=-\frac{N({{\varphi }_{2}}-{{\varphi }_{1}})}{\Delta t}=-\frac{NA({{B}_{2}}-{{B}_{1}})\cos \theta }{\Delta t}\]
\[=-\frac{NBA(\cos {{\theta }_{2}}-\cos {{\theta }_{1}})}{\Delta t}\]
Induced i, q and P
| Induced current (i) | Induced charge (q) | Induced power (P) |
| \[i=\frac{e}{R}=-\frac{N}{R}.\frac{d\varphi }{dt}\] | \[dq=i\,dt=-\frac{N}{R}\cdot d\varphi \] Induced charge is time independent. | \[P=\frac{{{e}^{2}}}{R}\]\[=\frac{{{N}^{2}}}{R}{{\left( \frac{d\varphi }{dt} \right)}^{2}}\] It depends on time and resistance |
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