Skip to main content

Visit this link for 1 : 1 LIVE Classes.

Conducting Bar Across $R_1$ & $R_2$

A conducting bar PQ is free to slide on two parallel conducting rails as shown in figure. Two resistors $R_1$ and $R_2$ are connected across the ends of the rails. There is a uniform magnetic field B pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents $I_1$ and $I_2$ flowing through $R_1$ and $R_2$ respectively is:


(A) $I_1$ is in anticlockwise direction and $I_2$ is in clockwise direction
(B) Both $I_1$ and $I_2$ are in anticlockwise direction
(C) Both $I_1$ and $I_2$ are in clockwise direction
(D) $I_1$ is in clockwise direction and $I_2$ is in anticlockwise direction

[Based on JEE Main 2021]
Solution

As PQ moves leftwards, the area of loop ABQP decreases causing reduction in flux. So, the direction of current through $R_1$ should be such that the flux can be increased. An upward current through $R_1$ helps to strengthen the magnetic field. Upward current through $R_1$ is the clockwise current through the left loop.

As PQ moves leftwards, the area of loop A'B'QP increases causing increase in flux. So, the direction of current  through $R_2$ should be such that the flux can be decreased. An upward current through $R_2$ helps to weaken the magnetic field. Upward current through $R_2$ is the anticlockwise current through the right loop.

Hence, Option (D).

Popular posts from this blog

${\log _{\sqrt 5 }}\left[ {3 + \cos \left( {\frac{{3\pi }}{4} + x} \right) + \cos \left( {\frac{\pi }{4} + x} \right) + \cos \left( {\frac{\pi }{4} - x} \right) - \cos \left( {\frac{{3\pi }}{4} - x} \right)} \right]$

The range of the function $f(x) = {\log _{\sqrt 5 }}\left[ {3 + \cos \left( {\frac{{3\pi }}{4} + x} \right) + \cos \left( {\frac{\pi }{4} + x} \right) + \cos \left( {\frac{\pi }{4} - x} \right) - \cos \left( {\frac{{3\pi }}{4} - x} \right)} \right]$ is: (A) $[ - 2,2]$ (B) $\left[ {\frac{1}{{\sqrt 5 }},\sqrt 5 } \right]$ (C) $(0,\sqrt 5 )$ (D) $[ 0,2]$ Solution We have, $f(x) = {\log _{\sqrt 5 }}\left( {3 - 2\sin \frac{{3\pi }}{4}\sin x + 2\cos \frac{\pi }{4}\cos x} \right)$ $ \Rightarrow f(x) = {\log _{\sqrt 5 }}\left[ {3 + \sqrt 2 (\cos x - \sin x)} \right]$ Now, $ - \sqrt 2  \le \cos x - \sin x \le \sqrt 2 $ $\therefore - 2 \le \sqrt 2 (\cos x - \sin x) \le 2$ $\therefore 1 \le 3 + \sqrt 2 (\cos x - \sin x) \le 5$ $\therefore{\log _{\sqrt 5 }}1 \le {\log _{\sqrt 5 }}[3 + \sqrt 2 (\cos x - \sin x)] \le {\log _{\sqrt 5 }}5$ $ \Rightarrow 0 \le f(x) \le 2$ Answer: (D)
Read more