Question

The electric current in a circular coil of two turns produced a magnetic induction of 0.2 T at its centre. The coil of 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)

0.8 T

Answer 2

When there are two turns in the coil, then

Then

When there are four turns in the coil, then

$1 = 4 \times 2 \pi r _ { 2 }$ or $r _ { 2 } = \frac { 1 } { 8 \pi }$

Then $B _ { 2 } = \frac { \mu _ { 0 } \mathrm {~N} _ { 2 } \mathrm { I } } { 2 \mathrm { r } _ { 2 } } = \frac { \mu _ { 0 } \times 4 \times \mathrm { I } } { 2 \times ( 1 / 8 \pi ) } = \frac { \mu _ { 0 } 16 \pi \mathrm { rl } } { 1 }$