A particle with charge q and mass m enters the shaded region through a narrow ho

Question

A particle with charge q and mass m enters the shaded region through a narrow hole (Figure 1) . In the shaded region there is a magnetic field B that points into the page. The particle is subject to both the force of magnetism and the force of gravity, yet travels in a straight line to the exit hole. Once it leaves the shaded region out the exit hole it is no longer in a magnetic field, but it still feels the force of gravity. The exit hole is a height h above the floor. Find the horizontal distance the particle travels before hitting the floor. Express x in terms of q, m, B, h, and g.

Explanation / Answer

Let the speed of the particle be v.

qvB=mg

v=mg/qB

Time of flight outside the hole=sqrt(2h/g)

Horizontal distance=vt=(m/qB)*sqrt(2gh)

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