There are two coils $\mathrm{A}$ and $\mathrm{B}$ separated by some distance. If a current of $2\mathrm{A}$ flows through $\mathrm{A}$, a magnetic flux of $10^{-2}\mathrm{Wb}$ passes through $\mathrm{B}$ ( no current through $\mathrm{B}$ ). If no current passes through $\mathrm{A}$ and a current of $1\mathrm{A}$ passes through $\mathrm{B}$, what is the flux through $\mathrm{A}$ ?
There are two coils $\mathrm{A}$ and $\mathrm{B}$ separated by some distance. If a current of $2\mathrm{A}$ flows through $\mathrm{A}$, a magnetic flux of $10^{-2}\mathrm{Wb}$ passes through $\mathrm{B}$ ( no current through $\mathrm{B}$ ). If no current passes through $\mathrm{A}$ and a current of $1\mathrm{A}$ passes through $\mathrm{B}$, what is the flux through $\mathrm{A}$ ?
Mutual inductance of system of coil A and coil B is, $\mathrm{M}_{21}=\frac{\phi_{2}}{\mathrm{I}_{1}}=\frac{10^{-2}}{2}$ $\mathrm{M}_{21}=5 \times 10^{-3} \mathrm{H}$
$\mathrm{M}_{21}=5 \times 10^{-3} \mathrm{H}$ Now $\mathrm{M}_{21}=\mathrm{M}_{12}=5 \times 10^{-3} \mathrm{H}$, but
$\mathrm{M}_{12}=\frac{\phi_{1}}{\mathrm{I}_{2}}$
$\therefore \phi_{1}=\mathrm{M}_{12} \mathrm{I}_{2} \quad\left[\because \mathrm{M}_{12}=\mathrm{M}_{21}\right]$
$=5 \times 10^{-3} \times 1$
$\phi_{1}=5 \times 10^{-3} \mathrm{~Wb}=5 \mathrm{~mW} b$
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