Physics Question on magnetic field - TPR FL

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geauxmed

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Here's the original question:
Increasing the magnitude of the voltage between the dees would have which of the following effects on the period of the particle’s revolutions in the cyclotron?
A) The period would decrease.
B) The period would increase.
C) The period would remain unchanged.
D) No prediction can be made.
From the passage:
It can be shown that T, the period of each complete revolution of the charged particle, is independent of the particle’s speed and is given by the equation

T =
3_P15444_1.gif


where m is the mass of the particle.

Since period is inversely proportional to the magnetic field, I thought voltage would cause a decrease, since B is proportional to I which is also proportional to voltage (Ohm's Law).

The correct answer however is C:

The equation given in the passage for the period T does not involve the magnitude of the voltage; T depends only on the mass and charge of the particle and the strength of the magnetic field. Therefore, since T is independent of V, we can predict that changing V will have no effect on T.

Could someone explain to me why my thought process is incorrect?

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