A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2Ω then the force needed to move the rod towards right with constant speed (v) of 1.5 m·s⁻¹ i $s ________$ N.

Question

G1 Physics · Accepted Answer

The motional emf induced across the rod is ε = Blv. Therefore the current in the circuit is i = Blv ───── R . The magnetic force on the rod is F₍ʙ₎ = Bil. To maintain constant speed, the applied external force must balance this magnetic force: F₍ext₎ = F₍ʙ₎. Hence, F₍ext₎ = B l × Blv ───── R = B²l²v ─────── R . Substitute B = 0.10 T, l = 1 m, v = 1.5 m·s⁻¹, R = 2 Ω. Thus, F₍ext₎ = (0.10)²(1)²(1.5) ─────────────── 2 = 7.5 × 10⁻³ N. Correct option: D.

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2Ω then the force needed to move the rod towards right with constant speed (v) of 1.5 m·s⁻¹ i s ________ N.