Two coaxial coils are very close to each other and their mutual inductance is $5 \,mH$. If a current $i = 50 \sin(500t) \,A$ is passed in one of the coils,then the peak value of the induced e.m.f. in the secondary coil will be ........... $V$.

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows 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 given above?

If a change in current of $0.01 \,A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} \,Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $\,H$)

There are two long coaxial solenoids of the same length $l$. The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self-inductance of the inner coil is

The induction coil works on the principle of

When a current of $4 \,A$ changes to $8 \,A$ in $0.6 \,s$ in a primary coil, it induces an e.m.f. of $50 \,mV$ in the secondary coil. The mutual inductance between the two coils is: (in $\,mH$)