An electric current $i_1$ can flow either direction through loop $(1)$ and induced current $i_2$ in loop $(2)$. Positive $i_1$ is when current is from $'a'$ to $'b'$ in loop $(1)$ and positive $i_2$ is when the current is from $'c'$ to $'d'$ in loop $(2)$ In an experiment, the graph of $i_2$ against time $'t'$ is as shown below Which one $(s)$ of the following graphs could have caused $i_2$ to behave as give above.

A circular wire loop of radius $R$ is placed in the $x$-y plane centered at the origin $O. A$ square loop os side $a ( a << R$ ) having two turns is placed with its center at $a=\sqrt{3} \ R$ along the axis of the circular wire loop, as shown in 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

What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times {10^{ - 2}}\,Wb$ and change in current is $0.01\,A$......$henry$

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

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

$\mu_{0}=4 \pi \times 10^{-7} \;TmA ^{-1}$

An $e.m.f.$ of $100\,millivolts$ is induced in a coil when the current in another nearby coil becomes $10\, ampere$ from zero in $0.1\,second$ . The coefficient of mutual induction between the two coils will be.....$millihenry$