(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

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(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 $\phi = B \times A_{1} = \left( \frac{\mu_{0} i}{2 R_{2}} \right) (\pi R_{1}^{2})$. By definition,the mutual inductance $M$ is given by $M = \frac{\phi}{i} = \frac{\mu_{0} \pi R_{1}^{2}}{2 R_{2}}$. Therefore,$M \propto \frac{R_{1}^{2}}{R_{2}}$.

Class 12 Physics Electromagnetic Induction Mutual Induction

Medium

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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A
$\frac{1}{R_{1} R_{2}}$
B
$\frac{R_{2}^{2}}{R_{1}}$
C
$R_{1} R_{2}$
D
$\frac{R_{1}^{2}}{R_{2}}$

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Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

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Alternating current of peak value $(\frac{2}{\pi}) \ A$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \ H$. The peak e.m.f. induced in the secondary coil is (Frequency of a.c. $= 50 \ Hz$) (in $V$)

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If the current $30 \,A$ flowing in the primary coil is made zero in $0.1 \,s$,the $e.m.f.$ induced in the secondary coil is $1.5 \,V$. The mutual inductance between the coils is.....$H$.

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Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \ cm^2$ and length $\ell = 20 \ cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \ T \ m \ A^{-1}$):

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Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).

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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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Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

Alternating current of peak value $(\frac{2}{\pi}) \ A$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \ H$. The peak e.m.f. induced in the secondary coil is (Frequency of a.c. $= 50 \ Hz$) (in $V$)

If the current $30 \,A$ flowing in the primary coil is made zero in $0.1 \,s$,the $e.m.f.$ induced in the secondary coil is $1.5 \,V$. The mutual inductance between the coils is.....$H$.

Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).

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