Question 247: Magnetism and Matter

Question

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $$B.$$ It is then bent into a circular loop of $$n$$ turns. The magnetic field at the center of the coil will be

Accepted Answer

KEY CONCEPT :
Magnetic field at the center of a circular coil of radius $$R$$ carrying
current is  $$B = {{{\mu _0}i} \over {2R}}$$
Given: $$n 	imes \left( {2\pi r'} ight) = 2\pi R$$
$$ \Rightarrow nr' = R\,\,\,\,\,\,\,\,\,\,\,...\left( 1 ight)$$
$$B' = {{n.{\mu _0}i} \over {2r'}}\,\,\,\,\,\,\,\,\,\,\,...\left( 2 ight)$$
from $$\left( 1 ight)$$ and $$\left( 2 ight),$$ $$B' = {{n{\mu _0}i.n} \over {2\pi R}} = {n^2}B$$

Answer

$$2n$$ $$B$$

Answer

$${n^2}\,B$$

Answer

$$nB$$

Answer

$$2{n^2}\,B$$

Magnetism and Matter

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B. It is then bent into a circular loop of n$ turns. The magnetic field at the center of the coil will be

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