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.

Solution

Physics sir · 4 steps

Flux changes only while PQ is inside the field. Then ask which graph is allowed to go negative.

1. Flux. The field covers only 0 ≤ x ≤ b, so while PQ moves out from 0 to b the flux φ = Blx rises linearly. From b to 2b and back to b, the area inside the field stays fixed, so φ is constant. It then falls linearly from b back to 0, which is graph A.

   ε = -dφ/dt = -Bldx/dt, P = ε²/R

2. EMF. At constant speed, ε has magnitude Blv only while PQ is inside the field, and it is zero where the flux is constant. The flux increases on the way out and decreases on the way back, so the EMF reverses sign. That matches graph B: a negative level, then zero, then a positive level.
3. Power. Power depends on ε², so it can never be negative. It equals B²l²v²/R on both trips through the field and is zero in between. That is graph C, with the same height on both sides.
4. So. A is flux, B is EMF and C is power dissipated. The answer is option (b).

The idea to keep. EMF follows the slope of the flux graph, so it flips sign when the flux turns from rising to falling. Power goes as ε², so it is always positive.

Answer from the NTA final answer key. Solution by PrepWiser.