Question 211: 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 (BL) to that at the center of the coil (BC),  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

N2

Answer

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

Magnetism and Matter

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