Two coaxial coils A and B of radii R_{1} and | vedclass

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Question

(D) The magnetic field $B$ at the center of the smaller coil $A$ due to the current $i$ in the larger coil $B$ is approximately uniform over the area

Vedclass · Accepted Answer

$\frac{R_{1}^{2}}{R_{2}}$

Vedclass · Answer

(D) The magnetic field $B$ at the center of the smaller coil $A$ due to the current $i$ in the larger coil $B$ is approximately uniform over the area of coil $A$. The magnetic field produced by coil $B$ at its center is $B = \frac{\mu_{0} i}{2 R_{2}}$. The magnetic flux $\phi$ linked with the smaller coil $A$ is $\phi = B 	imes A_{1} = \left( \frac{\mu_{0} i}{2 R_{2}} ight) (\pi R_{1}^{2})$. By definition,the mutual inductance $M$ is given by $M = \frac{\phi}{i} = \frac{\mu_{0} \pi R_{1}^{2}}{2 R_{2}}$. Therefore,$M \propto \frac{R_{1}^{2}}{R_{2}}$.

Two coaxial coils $A$ and $B$ of radii $R_{1}$ and $R_{2}$ are placed in the same plane $(R_{2} > R_{1})$. If a current is passed through coil $B$,the coefficient of mutual inductance between the coils is proportional to:

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