Question

The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its center. The coil is unwound and rewound in to a coil of four turns. The magnetic induction at the center of the coil now is, in tesla (if the same current flows in the coil)______​

Answer 1

Answer:

0.8T

Explanation:

When there are two turns in the coil, then

l=2×2πr1 or r1 =l/4π

When there are four turns in the coil, then

$l=4*2\pi r_{2} or \\r_{2} =l/8\pi$

B2=u0N2I2/2r2

    =u016piI/l

B1/B2=4/16

         =1/4

B2=4B1

   =4*0.2T

    =0.8T

Answer 2

Given : The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its center. The coil is unwound and rewound in to a coil of four turns.

To find : The magnetic induction at the centre of the coil now. (if the same current flows in the coil)

solution : let L is length of coil.

case 1 : for two turns of coil.

L = N × 2πr₁ = 2 × 2πr₁⇒r₁ = L/4π

magnetic induction at the centre of coil, B₁ = μN₁I/2r₁

⇒0.2T = μ × 2 × I/2(L/4π) = μ4πI/L........(1)

case 2 : for four turns of coil.

L = 4 × 2πr₂ ⇒r₂ = L/8π

new magnetic induction at the centre of coil, B₂ = μN₂I/r₂ = μ × 4 × I/2(L/8π) = μ16πI/L .......(2)

from equations (1) and (2) we get,

0.2T/B₂ = 1/4

⇒B₂ = 0.8T

Therefore the magnetic induction at the centre of the coil now is 0.8T