In a $dc$ motor, induced $e.m.f.$ will be maximum

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$

Two coils $P$ and $Q$ are separated by some distance. When a current of $3\, A$ flows through coil $P$ a magnetic flux of $10^{-3}\, Wb$ passes through $Q$. No current is passed through $Q$. When no current passes through $P$ and a current of $2\, A$ passes through $Q$, the flux through $P$ is

Two coils have a mutual inductance $0.005\,H$ . The current changes in the first coil The current changes in the first coil 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

A circular loop ofradius $0.3\ cm$ lies parallel to amuch bigger circular loop ofradius $20\ cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15\ cm$. If a current of $2.0\ A$ flows through the smaller loop, then the flux linked with bigger loop is

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

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