Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).

Two concentric circular coils,one of small radius $r$ and the other of large radius $R$,are placed coaxially with their centers coinciding. If the radius $r$ is changed by $2 \%$,then the change in mutual inductance of the arrangement is (assume $r \ll R$). (in $\%$)

Two coils have a mutual inductance of $0.005\,H$. The current in the first coil changes according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10\,A$ and $\omega = 100\pi \,rad/s$. The maximum value of $emf$ in the second coil will be: (in $\pi \,V$)

Two conducting circular loops $A$ and $B$ are placed in the same plane with their centres coinciding as shown in the figure. If $b >> a$,the mutual inductance between them is:

The coefficient of mutual inductance,when magnetic flux changes by $2 \times 10^{-2} \ Wb$ and current changes by $0.01 \ A$,is ... $H$.

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?