A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I = I_0\, cos\, (\omega t)$ . The emf induced in the smaller inner loop is nearly
$\frac{{\pi {\mu _0}{I_0}}}{2}.\frac{{{a^2}}}{b}\omega \,\sin \,\left( {\omega t} \right)$
$\frac{{\pi {\mu _0}{I_0}}}{2}.\frac{{{a^2}}}{b}\omega \,\cos \,\left( {\omega t} \right)$
$\pi {\mu _0}{I_0}\,\frac{{{a^2}}}{b}\omega \,\sin \,\left( {\omega t} \right)$
$\frac{{\pi {\mu _0}{I_0}{b^2}}}{a}\,\omega \,\cos \,\left( {\omega t} \right)$
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10\ cm^2$ and length$= 20\ cm$. If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is
$\mu_{0}=4 \pi \times 10^{-7} \;TmA ^{-1}$
A coil of radius $1\, cm$ and of turns $100$ is placed in the middle of a long solenoid of radius $5\, cm$. and having $5\, turns/cm$. parallel to the axis of solenoid The mutual inductance in millihenery will be
In $SI$, Henry is the unit of
If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times {10^{ - 2}}\,Wb$ in the other coil, then the mutual inductance of the two coils in henries is.....$H$
A small square loop of wire of side $l$ is placed inside a large square loop of wire $L(L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is.