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:
Answer: (C) A—Flux, B—EMF, C—Power dissipated
Let the arm have length $l$ and move at constant speed $v$.
Flux: $\phi = Blx$ for $x < b$, then constant $Blb$ while the arm is outside the field, and it falls back linearly on the return through the field. This is graph A.
EMF: $Blv$ while the arm is in the field and zero outside; on the return the flux decreases, so the EMF has the opposite sign. This is graph B.
Power $\dfrac{\varepsilon^2}{R}$ is the same positive value whenever the arm is in the field, both going out and coming back, and zero otherwise. This is graph C.
Solution by Sreeraj P, M.Sc Physics