An electron in motion with a constant velocity v⃗ enters a uniform magnetic field B perpendicularly. Given that mₑ, e, v represent the mass, charge, and magnitude of the electron's velocity respectively, which of the following statements is false?
A) The motion of the electron is uniformly circular with a period of 2πmₑ/(eB)
B) The trajectory of the electron is a circle with a radius of mₑv/(eB)
C) The motion of the electron is circular with constant angular velocity
D) The electron continues to move with a constant velocity v⃗
E) The motion of the electron is uniformly circular with a frequency eB/(2πmₑ)
IMAT 2024 · Question 58
Q58 - Magnetic effects of current
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The correct answer is D) The electron continues to move with a constant velocity v⃗.
A magnetic force is always at right angles to the motion, so it changes the electron's direction but never its speed. The electron goes round in a circle at constant speed.
That makes D the false one: the velocity doesn't stay constant, because velocity includes direction and the direction keeps changing. The radius, period, frequency and constant angular velocity in the other options are all correct.
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