The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b… | JEE Main 2021 (20 Jul, Shift 1)

Q43JEE Main 2021 · 20 JUL · SHIFT 1Difficult

Motional EMF

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance.

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Answer: (b)

Flux: rises linearly from $0$ to $b$ (area in field grows), stays constant from $b$ to $2b$ and back to $b$ , then falls to zero. This is graph A.
EMF $= -\dfrac{d\phi}{dt}$ : constant while going out ( $0$ to $b$ ), zero outside the field, constant with opposite sign while coming back. This is graph B.
Power $= \dfrac{e^2}{R}$ : same positive value in both field stretches, zero elsewhere. This is graph C.
So the answer is (b) A-Flux, B-EMF, C-Power dissipated.

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