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Two wires of same material and same length 20 cm are wound in the form of two coils A and B. The coil A has 4 turns and the coil B has 2 turns. If same current is sent into the two coils, the ratio of magnetic induction at the centers of the two coils A and B is

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$4 : 1$

$1 : 4$

$2 : 1$

$1 : 2$

answer is A.

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Detailed Solution

When the length of the wire is constant, the magnetic field at the center of the coil is directly proportional to the square of the no of turns in the coil.

$h e r e \frac{n_{1}}{n_{2}} = \frac{2}{1}; \frac{B_{1}}{B_{2}} = 4 : 1$

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