A charged particle moves in the x A charged particle moves in the xa??y plane, a

Question

A charged particle moves in the x

A charged particle moves in the xa??y plane, and a magnetic field B is directed into the plane as shown in the figure below. The magnetic force on the particle causes the particle to move clockwise along a circle of radius R. (a) The charge of the particle is increased by a factor of seven, and the particle is found to move in a circle of radius R'. What is the ratio R'/R? (b) The mass of the particle is decreased by a factor of four, and the particle is found to move in a circle of radius R''. What is the ratio R/R?

Explanation / Answer

Answer:  Force on the charge due to magnetic field provides the centripetal force for circular motion
=> qvB = mv^2/R
=> R = mv/qB

=> R is inversely proportional to charge
=> when charge is increased by a factor of seven, radius decreases by the same factor
=> R'/R = 1/7

Also, R is directly proportional to mass
=> when the mass is decreased by a factor of 8, then R also decreases by a factor of 8
=> R'/R = 1/8.

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