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A particle of charge q and mass m is moving with a velocity -v î (v ≠ 0) towards a large screen placed in the Y-Z plane at a distance d. If there is a magnetic field B = B0 k̂, the minimum value of v for which the particle will not hit the screen is:

1. (1) qdB0/2m
2. (2) 2qdB0/m
3. (3) qdB0/3m
4. (4) qdB0/m

Correct answer: (4) qdB0/m

Solution

The particle follows a circular arc whose maximum penetration toward the screen equals its radius r = mv/(qB0). It just fails to reach a screen at distance d when r = d, giving the critical speed v = qdB0/m.

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