Question

When a magnet is moved quickly towards a closed coil the induced emf and charge are `e' and `q'. When the same magnet is slowly towards the same coil, the induced emf and charge are $e^1$ and $q^1$ respectively. Then

• A. $e>e^1,q>q^1$
• B. $e>e^1,q=q^1$
  
• C. $e=e^1,q=q^1$
  
• D. $e<e^1,q<q^1$

Answer 1

The correct option is B $e>e^1,q=q^1$


$e=-\frac{d\varphi }{dt}$
If the magnet is moved slowly, induced emf will be less.
$\therefore e>e^1$
$i=\frac{|e|}{R}=\frac{1}{R}|\frac{d\varphi }{dt}|$
$\Rightarrow \frac{dq}{dt}=\frac{1}{R}|\frac{d\varphi }{dt}|$
$\therefore q=\frac{1}{R}|\Delta \varphi |$
$\therefore q^1=q$ as the charge does not depend on the time.