There are two coils $\mathrm{A}$ and $\mathrm{B}$ separated by some distance. If a current of $2\mathrm{A}$ flows through $\mathrm{A}$, a magnetic flux of $10^{-2}\mathrm{Wb}$ passes through $\mathrm{B}$ ( no current through $\mathrm{B}$ ). If no current passes through $\mathrm{A}$ and a current of $1\mathrm{A}$ passes through $\mathrm{B}$, what is the flux through $\mathrm{A}$ ?
Mutual inductance of system of coil A and coil B is, $\mathrm{M}_{21}=\frac{\phi_{2}}{\mathrm{I}_{1}}=\frac{10^{-2}}{2}$ $\mathrm{M}_{21}=5 \times 10^{-3} \mathrm{H}$
$\mathrm{M}_{21}=5 \times 10^{-3} \mathrm{H}$ Now $\mathrm{M}_{21}=\mathrm{M}_{12}=5 \times 10^{-3} \mathrm{H}$, but
$\mathrm{M}_{12}=\frac{\phi_{1}}{\mathrm{I}_{2}}$
$\therefore \phi_{1}=\mathrm{M}_{12} \mathrm{I}_{2} \quad\left[\because \mathrm{M}_{12}=\mathrm{M}_{21}\right]$
$=5 \times 10^{-3} \times 1$
$\phi_{1}=5 \times 10^{-3} \mathrm{~Wb}=5 \mathrm{~mW} b$
There are two long co -axial solenoids of same length $l.$ The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self -inductance of the inner -coil is
Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' $R$ ' is placed inside a large square loop of wire of side $L$ $( L \gg R )$. The loops are coplanar and their centres coincide :
If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times {10^{ - 2}}\,Wb$ in the other coil, then the mutual inductance of the two coils in henries is.....$H$
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
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 $2A$ in the solenoid is reversed in $0.25\, sec$, then the $e.m.f$. induced in the coil is