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Magnetic Field Due to a Circular Arc at the Centre

A circular co...

Question

A circular coil A of radius r carries current i. Another circular coil B of radius 2r carries current of i. The magnetic fields at the centres of the circular coils are in the ratio of

3 : 1

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4 : 1

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1 : 1

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2 : 1

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Solution

The correct option is C 2 : 1
Magnetic field at center of circular coil is given as
$B = \frac{μ n i}{2 r}$
from above formula when $i$ is kept constant.
$\begin{matrix} B \propto \frac{1}{r} \frac{B_{1}}{B_{2}} = \frac{r_{2}}{r_{1}} r_{1} = r r_{2} = 2 r \end{matrix}$
Therefore $B_{1} : B_{2} = 2 : 1$
$∴$ Option $D$ is correct.

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A circular coil A of radius r carries current i. Another circular coil B of radius 2r carries current of i. The magnetic fields at the centres of the circular coils are in the ratio of

The correct option is C 2 : 1Magnetic field at center of circular coil is given asB=μni2rfrom above formula when i is kept constant.B∝1rB1B2=r2r1r1=rr2=2rTherefore B1:B2=2:1∴ Option D is correct.