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Physics · 2023 · 3 marks
CBSE 2023 · Region 3 · Set 3 · Q28
The figure shows a rectangular conductor PQRS in which the arm PQ of length 10 cm and resistance 0 · 4 Ω is free to move. It is kept in a uniform…
The figure shows a rectangular conductor PQRS in which the arm PQ of length $\displaystyle 10$ cm and resistance $\displaystyle 0 \cdot 4 \Omega$ is free to move. It is kept in a uniform magnetic field $\displaystyle \mathrm{B}=0 \cdot 2 \mathrm{~T}$ acting perpendicular into the plane of PQRS . If $\displaystyle \operatorname{arm} \mathrm{PQ}$ is moved with a velocity v of $\displaystyle 5 \mathrm{~cm} / \mathrm{s}$ as shown, find :
(a)
the current induced in the loop, and
(b)
the power required to move the arm. (Resistances of arms PS, SR and RQ are negligible.)
Marking-scheme solution
Finding the
(a)
\[\begin{aligned}
& i=\frac{\mathrm{B} l \mathrm{v}}{R} \\
& =\frac{0.2 \times\left(10 \times 10^{-2}\right) \times\left(5 \times 10^{-2}\right)}{0.4} \\
& i=2.5 \times 10^{-3} \mathrm{~A}
\end{aligned}
\]
(b)
\[\begin{aligned}
& P=i^{2} R \\
& =\left(2.5 \times 10^{-3}\right)^{2} \times 0.4 \\
& P=2.5 \times 10^{-6} \mathrm{~W}
\end{aligned}
\]
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