A short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length $L$, radius $R$ and $N$ turns per unit length, with $R>r$ ). Current $I$ follows in the short solenoid. Choose the correct statement.
There is uniform magnetic field $\mu_{0} n I$ in the long solenoid.
Mutual inductance of the solenoids is $\pi \mu_{ 0 } r^{2} n N l$.
Flux through outer solenoid due to current $I$ in the inner solenoid is proportional to the ratio $R / r$.
Mutual inductance of the solenoids is $\pi \mu_{0} r R n N l L /(r R)^{1 / 2} .$
In a transformer, the coefficient of mutual inductance between the primary and the secondary coil is $0.2 \,henry$. When the current changes by $5$ $ampere/second$ in the primary, the induced $e.m.f$. in the secondary will be......$V$
Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be
With the decrease of current in the primary coil from $2\,amperes$ to zero value in $0.01\,s$ the $emf$ generated in the secondary coil is $1000\,volts$. The mutual inductance of the two coils is......$H$
Two circuits have coefficient of mutual induction of $0.09$ $henry$. Average $e.m.f$. induced in the secondary by a change of current from $0$ to $20$ $ampere$ in $0.006$ $second$ in the primary will be......$V$
Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other, on passing a current of $3.0$ ampere in $A$, the flux linked with A is $1.2 \times {10^{ - 4}}\,weber$ and with $B$ it is $9.0 \times {10^{ - 5}}\,weber$. The mutual inductance of the system is