Question

Two circular coils $ P $ and $ Q $ are made from similar wire, but radius of $ Q $ is twice that of $ P $ . What should be the value of potential difference across them so that the magnetic induction at their centre may be same?

• A. $ V_q = 2V_p $
• B. $ V_q = 3 \,V_p $
• C. $ V_q = 4V_p $
• D. $ V_{q} = \frac{1}{4}\,V_{p} $

Answer 1

Answer: (C)

$B_{1}=\frac{\mu_{0}}{4 \pi}\left[\frac{2 \pi I_{1}}{r_{1}}\right]$ and $B_{2}=\frac{\mu_{0}}{4 \pi}\left[\frac{2 \pi I_{2}}{r_{2}}\right]$
Since, $B_{1}=B_{2}$ and $r_{2}=2 r_{1}, I_{2}=2 I_{1}$
$\therefore \,\,\, \frac{V_{2}}{V_{1}}=\frac{I_{2} R_{2}}{I_{1} R_{1}}=\frac{2 I_{1}}{I_{1}} \times \frac{2 R_{1}}{R_{1}}=\frac{4}{1}$