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Question:

A positive charge 'q' of mass 'm' is moving along the +x axis. We wish to apply a uniform magnetic field B for time Δt, so that the charge reverses its direction, crossing the y axis at a distance d. Then:

B=mvqdandΔt=πdv

B=2mvqdandΔt=πdv

B=mv2qdandΔt=πd2v

B=2mvqdandΔt=πd2v

Solution:

To change the direction of charge, a force needs to be applied such that, qvB = mv²/r where r = d/2. Therefore, B = 2mv/qd. Total displacement is d when charge travels for time, Δt. Therefore, Δt = πd/2v