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Physics · 2025 · 3 marks
CBSE 2025 · Region 7 · Set 2 · Q26
(a) Two concentric circular coils of radii r_1 and r_2(r_2 ≫ r) are placed coaxially with their centres coinciding. If a current I is passed through…
(a)
Two concentric circular coils of radii $\displaystyle r_{1}$ and $\displaystyle r_{2}\left(r_{2} \gg r\right)$ are placed coaxially with their centres coinciding. If a current I is passed through the outer coil, obtain the expression for mutual inductance of the arrangement.
(b)
The current in a solenoid decreases steadily from $\displaystyle 6$ mA to $\displaystyle 2$ mA in $\displaystyle 50$ ms . If an average emf of $\displaystyle 0.4$ V is induced, find the self-inductance of the solenoid.
Marking-scheme solution
(a)
Magnetic field at centre of outer coil $\displaystyle S_2$
\[B_2 = \frac{\mu_0 I_2}{2r_2} \]
Flux linked with inner coil $\displaystyle S_1$ is
\[\phi_1 = B_2 A_1 \]
\[= \frac{\mu_0 I_2}{2r_2}\,.\,\pi r_1^{\,2} \]
Also, $\displaystyle \phi_1 = M_{12} I_2$
\[\therefore M_{12} = \frac{\mu_0}{2r_2}\,.\,\pi r_1^{\,2} \]
(b)
$\displaystyle \varepsilon = -L\dfrac{dI}{dt}$
\[L = \frac{0.4 \times 50 \times 10^{-3}}{4 \times 10^{-3}} \]
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