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

0.2T

B

0.4T

C

0.6T

D

0.8T

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The correct Answer is:D

When there are two turns in the coil, then
$l = 2 \times 2 π r_{1} or r_{1} = \frac{l}{4 π}$
$then B_{1} = \frac{μ_{0} N_{1} I}{2 r_{1}} = \frac{μ_{0} 2 \times I}{2 \times (l / 4 π)} = \frac{μ_{0} 4 π I}{l}$
When there are four turns in the coil, then
$l = 4 \times π r_{2} or r_{2} = \frac{l}{8 π}$
$Then B_{2} = \frac{μ_{0} N_{2} I}{2 r_{2}} = \frac{μ_{0} \times 4 \times I}{2 \times (l / 8 π)} = \frac{μ_{0} 16 π l}{l}$
$\frac{B_{1}}{B_{2}} = \frac{4}{16} = \frac{1}{4} or B_{2} = 4 B_{1} = 4 \times 0.2 T = 0.8 T$

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Updated on:21/07/2023

Class 12 PHYSICS MOVING CHARGES AND MAGNETISM

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