Two particles with charges q and 2q moving from west to east enter a uniform mag

Question

Two particles with charges q and 2q moving from west to east enter a uniform magnetic ?eld of magnitude B pointing vertically down. The charges have different masses, but the same speed v. In the magnetic ?eld, they move in semicircles with radii R and 2R, respectively.

(a) What is the ratio of their masses?
(b) Is it possible to apply an electric ?eld that would cause the particle of charge q to move in a straight line in the magnetic ?eld? If yes, what is the direction and magnitude of this ?eld?
(c) What effect would this electric ?eld have on the particle of charge 2q?

Explanation / Answer

m v^2 / R = q v B centripetal force = magnetic force m = q B R / v m2 / m1 = q2 R2 / (q1 R1) = 2 * 2 = 4 If we choose E q = q v B (at right angles) then the magnetic force = the electric force E = v B and does not depend on the charge

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