In a velocity selector for ions, when the velocity of the ions is double the value for which the selector is set, how do the magnetic force F_M and the electric force F_E compare? A) F_M = 4 F_E B) F_M = 2 F_E C) F_M = F_E/2 D) F_M = F_E/4 E) F_M = 1.414 F_E

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Quizplus · Accepted Answer

In a velocity selector for ions, the magnetic force F_M and electric force F_E are of equal magnitude and opposite direction, so they cancel each other out to allow only ions of a specific velocity to pass through. When the velocity of the ions doubles, the electric force remains the same because it depends only on the charge and electric field, which are constant. However, the magnetic force depends on the velocity of the ions and the strength of the magnetic field, so it becomes four times larger (since velocity is squared in the formula for magnetic force). Therefore, the magnetic force is twice as large as the electric force, and the answer is B.

In a Velocity Selector for Ions, When the Velocity of the Ions