Question 220: Magnetism and Matter

Question

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central of the loop (B
L
) to that at the center of the coil (B
C
),  i.e. $${{{B_L}} \over {{B_C}}}$$ will be :

Accepted Answer

For loop,
L = 2$$\pi $$R
For coil,
L = N $$ 	imes $$ 2$$\pi $$r
$$ 	herefore $$   2$$\pi $$R = N $$ 	imes $$ 2$$\pi $$r
$$ \Rightarrow $$  R = Nr
$$ \Rightarrow $$  r = $${R \over N}$$
We know,
B
L
= $${{{\mu _0}i} \over {2R}}$$
and  B
C
= N $$ 	imes $$ $${{{\mu _0}i} \over {2r}}$$
$$ 	herefore $$  $${{{B_L}} \over {{B_C}}} = {{{{{\mu _0}i} \over {2R}}} \over {N 	imes {{{\mu _0}i} \over {2\left( {{R \over N}} ight)}}}} = {1 \over {{N^2}}}$$

Answer

N

Answer

$${1 \over N}$$

Answer

N
2

Answer

$${1 \over {{N^2}}}$$

Magnetism and Matter

Choose the correct answer: