Question

A length of wire carries a steady current, is bent first to form a plane circular coil of one turn, same length are bent more sharply to give three turns of smaller radius. Magnetic field becomes:-

• A. 4 times
• B. 1/3 times
• C. 9 times
• D. uncharged

Answer 1

The correct option is

C

9 times

Length of wire be $l$

$\Rightarrow$ The wire is bent in form of circular loop

In case (i)

Let the radius of the loop be $R$

$\therefore$ $2\pi R=l$ $\Rightarrow$ $R=\frac{l}{2\pi }$

In case (ii)

the same lengh is bent to form another loop with 3 turns

$3\times 2\pi r=l$

$\therefore$ $r=\frac{l}{6\pi }$

In case (i)

$B_i=N\frac{{\mu }_{0}i}{2R}$

$N=1$

$B_1=\frac{{\mu }_{0}i}{\frac{l}{\pi }}=\frac{{\mu }_{0}i\pi }{l};$

$incase\left(2\right)N_2=3;B_2=\frac{3{\mu }_{0}i}{2r}=\frac{{9\mu }_{0}i\pi }{l}$

$\therefore \frac{B_1}{B_2}=\frac{\frac{{\mu }_{0}i\pi }{l}}{\frac{{9\mu }_{0}i\pi }{l}}=\frac{1}{9}$

$\Rightarrow \frac{B_2}{B_1}=9$