K K Sharma Solutions for Chapter: Electromagnetic Induction, Exercise 14: Mutual Inductance

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10 {\mathrm{cm}}^2$ and length $20 \mathrm{cm}$. If one of the solenoids has $300$ turns and the other has $400$ turns, their mutual inductance is $\left({\mu }_0=4\mathrm{\pi }\times {10}^{-7 }\mathrm{T} \mathrm{m} {\mathrm{A}}^{-1}\right)$

A circular wire loop of radius $R$, is placed in an $X-Y$ plane, Centre at the origin $O$. A square loop of side $a \left(a<<R\right)$, having two turns, is placed with its center at $z=\sqrt{3}R$, along the axis of circular wire loop, as shown in the figure. The plane of the square loop makes an angle of ${45}^{\circ }$ with respect to the $z$-axis. If the mutual inductance between the loops is given by $\frac{{\mu }_0{a}^2}{2^{p/2}R}$, then the value of $p$ is 

The mutual inductance of two coils is $1.25 \mathrm{H}$. In the first coil, if the current changes at $80 \mathrm{A} {\mathrm{s}}^{-1}$, then the value of induced EMF (in $\mathrm{volt}$) in the secondary coil will be 

Two coils have a mutual inductance of $0.005 \mathrm{H}$. The current changes in the first coil, according to the equation, $I=I_0\sin 𝝎t$, where $I_0=10 \mathrm{A}$ and $𝝎=100\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$. The maximum value of emf in the second coil will be

Two coils, $A$ and $B$, of $12500$ turns and $16000$ turns, respectively, lie in parallel planes so that, $60\%$ of flux produced in $A$ links with $B$. It is found that, a current of $5 \mathrm{A}$ in coil $A$ produces a flux of  $0.6 \mathrm{mWb}$, whereas the same current in coil $B$ produces a flux of $0.8 \mathrm{mWb}$. The mutual inductance of the two coils is 

Two coils of self inductance $2 \mathrm{mH}$ and $8 \mathrm{mH}$, respectively, are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is 

The mutual inductance of an induction coil is $5 \mathrm{H}$. In the primary coil, the current reduces from $5 \mathrm{A}$ to zero, in ${10}^{-3} \mathrm{s}$. What is the induced emf in the secondary coil?