Two conducting circular loops of radii $R_{1}$ and $R_{2}$ are placed in the same plane with their centres coinciding. If $R_{1} >> R_{2}$,the mutual inductance $M$ between them will be directly proportional to:

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is:

Two concentric coplanar circular conducting loops have radii $R$ and $r$ $(R \gg r)$. Their mutual inductance is proportional to

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?

Two coils are kept near each other. When no current passes through the first coil and the current in the $2^{nd}$ coil increases at the rate of $10 \,A/s$, the e.m.f. in the $1^{st}$ coil is $20 \,mV$. When no current passes through the $2^{nd}$ coil and $3.6 \,A$ current passes through the $1^{st}$ coil, the flux linkage in coil $2$ is:

Consider two coils in which a current in one coil carrying $6$ $A$ causes the change in the flux in the second coil $12 \times 10^{-4}$ $Wb/turn$. The second coil has $2000$ turns. The mutual inductance between the coils is (in $H$)