Faraday's Law Of Induction - Practice Questions & MCQ

 Faraday’s First Law-

Whenever the number of magnetic lines of force (Magnetic Flux) passing through a circuit changes an emf called induced emf is produced in the circuit. The induced emf persists only as long as there is a change of flux.

Faraday’s Second Law-

The induced emf is given by the rate of change of magnetic flux linked with the circuit.

i.e Rate of change of magnetic Flux $=\varepsilon=\frac{-d \phi}{d t}$
where $d \phi \rightarrow \phi_2-\phi_1=$ change in flux
And For N turns it is given as $\varepsilon=\frac{-N d \phi}{d t}$ where $\mathrm{N}=$ Number of turns in the Coil.
The negative sign indicates that induced emf (e) opposes the change of flux. And this Flux may change with time in several ways
I.e As $\phi=B A \cos \Theta$ so $\varepsilon=N \frac{-d}{d t}(B A \cos \Theta)$
1.If Area (A) change then $\varepsilon=-N B \cos \Theta\left(\frac{d A}{d t}\right)$
2.If Magnetic field (B) change then $\varepsilon=-N A \cos \Theta\left(\frac{d B}{d t}\right)$
3. If Angle ( $\theta$ ) change then $\varepsilon=-N A B \frac{d(\cos \Theta)}{d \Theta} \times \frac{d \Theta}{d t}$ or $\varepsilon=+N B A \omega \sin \Theta$

• Induced Current- 

$
I=\frac{\varepsilon}{R}=\frac{-N}{R} \frac{d \phi}{d t}
$

where
$R \rightarrow$ Resistance
$\frac{d \phi}{d t} \rightarrow$ Rate of change of flux
- Induced Charge-

$
\begin{aligned}
& d q=i . d t=\frac{-N}{R} \frac{d \phi}{d t} \cdot d t \\
& d q=\frac{-N}{R} d \phi
\end{aligned}
$

I.e Induced Charge time-independent.
- Induced Power-

$
P=\frac{\varepsilon^2}{R}=\frac{N^2}{R}\left(\frac{d \phi}{d t}\right)^2
$
 

      i.e - Induced Power depends on both time and resistance