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Two identical conducting rods are placed perpendicular to two smooth parallel rails in a uniform magnetic field B on a horizontal table. The right rod is initially at rest and the left rod is given an initial velocity v0. Each rod has resistance R. After a long time, both rods reach the same final velocity v0/n. Find n.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

The magnetic braking force is internal to the two-rod system, so total linear momentum is conserved. Initially only the left rod moves: p_i = m*v0. At equilibrium both rods move at v_f: p_f = 2m*v_f. By conservation: v_f = v0/2, so n = 2.

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