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

The correct option is D 0.8 T

When there are two turns in the coil, then
$l=2\times 2\pi r_1$ or $r_1=\frac{l}{4\pi }$

then $B_1=\frac{{\mu }_o{N}_{1}I}{2r_1}=\frac{{\mu }_o\times 2\times I}{2\times \left(l/4\pi \right)}=\frac{{\mu }_{o}4\pi I}{l}$

When there are four turns in the coil, then
$l=4\times 2\pi r_2$ or $r_2=\frac{l}{8\pi }$

Then $B_2=\frac{{\mu }_o{N}_{2}I}{2r_2}=\frac{{\mu }_o\times 4\times I}{2\times \left(l/8\pi \right)}=\frac{{\mu }_{o}16\pi I}{l}$

$\frac{B_1}{B_2}=\frac{4}{16}=\frac{1}{4}=$ or $B_2=4B_1=4\times 0.2T=0.8T$