When magnetic flux changes from $6.5 \times 10^{-2} \ Wb$ to $11 \times 10^{-2} \ Wb$ and the change in current is $0.03 \ A$,the coefficient of mutual inductance will be: (in $H$)

Explain mutual induction and derive the equation for mutual $emf$.

$A$ circular loop of radius $0.3 \, cm$ lies parallel to a much bigger circular loop of radius $20 \, cm$. 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 $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is:

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn,$\mu_0 =$ permeability of free space).

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ($\mu_0 =$ permeability of free space) (Both coils have single turn).

Two coils have a mutual inductance of $0.005 \text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 60\pi \text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil in volt will be (in $\pi$)