Question

The electric current in a circular coil of two turns produced a magnetic induction of $0.2T$ 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. $0.8T$

Answer 1

Answer: (D)

When there are two turns in the coil, then
$l=2\times 2\pi r_1$ or $r_1=\frac{l}{4\pi }$
then $B_1=\frac{{\mu }_0{N}_{1}I}{2r_1}=\frac{{\mu }_0\times 2\times I}{2\times \left(l/4\pi \right)}=\frac{{\mu }_{0}4\pi I}{l}$
When there are four turns in the coil, then
$l=4\times 2\pi r_2$ or $r_2=\frac{l}{8\pi }$
Then $B_2=\frac{{\mu }_0{N}_{2}I}{2r_2}=\frac{{\mu }_0\times 4\times I}{2\times \left(l8\pi \right)}=\frac{{\mu }_{0}16\pi I}{l}$
$\frac{B_1}{B_2}=\frac{4}{16}=\frac{1}{4}$ or $B_2=4B_1=4\times 0.2T$
$=0.8T$