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Physics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 3 · Q30
A rectangular conductor MNPQ with a movable arm MN (resistance r ) is kept in a uniform magnetic field as shown in the figure. Resistance of arms MQ,…
A rectangular conductor MNPQ with a movable arm MN (resistance r ) is kept in a uniform magnetic field as shown in the figure. Resistance of arms $\displaystyle \mathrm{MQ}, \mathrm{QP}$ and PN are negligible. Obtain the expression for the :
(a)
current induced in the loop specifying its direction, and
(b)
power required to move the arm.
Marking-scheme solution
(a) (i)
(a)(i)
Magnetic flux enclosed by the loop MNPQ
\[\phi_{B}=B I x
\]
Since x is changing with time, the rate of change of flux \(\displaystyle \phi_{B}\) will induce an e.m.f. given by
\[\varepsilon=\frac{-d \phi_{B}}{d t}=-\frac{d}{d t}(B l x)
\]
\[|\varepsilon|=B l v
\]
Induced current in the loop
\[I=\frac{\varepsilon}{r}=\frac{B l v}{r}
\]
(ii)
Direction - anticlockwise or along NMQP
(b)
Power required
\[P=F v=I B l v
\]
\[P=\frac{B^{2} l^{2} v^{2}}{r}
\]
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CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.