Question

The electric current in a circular coil of two turns produced a magnetic induction of $0.2\, T$ at its centre. The coil is unwound and then rewound into a circular coil of four turns. If same current flows in the coil, the magnetic induction at the centre of the coil now is

• A. $0.2\, T$
• B. $0.4\, T$
• C. $0.6\,T$
• D. $0.8\, T$

Answer 1

Answer: (D)

When there are two turns in the coil, then
$l=2\times2\pi r_{1}$ or $r_{1}=\frac{l}{4\pi}$
then $B_{1}=\frac{\mu_{0} N_{1}I}{2r_{1}}=\frac{\mu_{0}\times2\times I}{2\times\left(l / 4\pi\right)}=\frac{\mu_{0}\,4\pi I}{l}$
When there are four turns in the coil, then
$l=4 \times2\pi r_{2}$ or $r_{2}=\frac{l}{8\pi}$
Then $B_{2}=\frac{\mu_{0}\, N_{2}I}{2r_{2}} = \frac{\mu_{0}\times4\times I}{2\times\left(l 8\pi\right)}=\frac{\mu_{0}\,16\pi I}{l}$
$\frac{B_{1}}{B_{2}}=\frac{4}{16}=\frac{1}{4}$ or $B_{2}=4B_{1}=4\times0.2\,T$
$=0.8\, T $