QJEEAdv23Ph4d12: JEE Advanced 2023 Physics - Class 12 JEEAdv23Ph4d12 Solution: A rectangular conducting loop of length and width is in the…

Question

Verified Solution • 2025–26 Session moderate

A rectangular conducting loop of length

4 \mathrm{~cm}

and width

2 \mathrm{~cm}

is in the

x y

-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction

\frac{\sqrt{3}}{2} \hat{x}+\frac{1}{2} \hat{y}

with a constant speed

\mathrm{v}

. The wire is carrying a steady current

I=10 \mathrm{~A}

in the positive

x

-direction. A current of

10 \mu \mathrm{A}

flows through the loop when it is at a distance

d=4 \mathrm{~cm}

from the wire. If the resistance of the loop is

0.1 \Omega

, then the value of

\mathrm{v}

is ________

\mathrm{m} \mathrm{s}^{-1}

.

[Given: The permeability of free space

\mu_0=4 \pi \times 10^{-7} \mathrm{~N} \mathrm{~A}^{-2}

]

Accepted Answer

\begin{aligned}&amp;R=0.1 \Omega\\\\&amp;\varepsilon=\left(\mathrm{B}_1-\mathrm{B}_2\right) b v_{\mathrm{y}}\\\\&amp;\begin{aligned}&amp; \mathrm{i}=\frac{\varepsilon}{R}=\frac{\mu_0 I}{2 \pi R}\left(\frac{1}{d}-\frac{1}{d+a}\right) b v_y \\\\&amp; \Rightarrow 10^{-5}=\frac{2 \times 10^{-7} \times 10}{0.1}\left[\frac{1}{4}-\frac{1}{8}\right] \times 2 . v_y\end{aligned}\end{aligned}

\therefore \mathrm{v}_{\mathrm{y}}=2

\begin{aligned}&amp; \tan \theta=\frac{\mathrm{v}_{\mathrm{y}}}{\mathrm{v}_{\mathrm{x}}}=\frac{1}{\sqrt{3}} \\\\&amp; \therefore \mathrm{v}_{\mathrm{x}}=2 \sqrt{3} \\\\&amp; \therefore \mathrm{v}=\sqrt{\mathrm{v}_{\mathrm{x}}^2+\mathrm{v}_{\mathrm{y}}^2}=4\end{aligned}

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