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Problem 1 - Olympiad

An electron is accelerated through a potential difference of 100 V and then subjected to a uniform magnetic field perpendicular to its motion. The radius of the circular path is found to be proportional to which of the following?

A. The square root of the accelerating voltageB. The inverse of the accelerating voltageC. The accelerating voltageD. The square of the accelerating voltage

Correct: A

The radius of the path (r) for an electron in a magnetic field is given by $ r = \frac{mv}{qB} $. Since kinetic energy $ eV = \frac{1}{2}mv^2 $, velocity $ v $ is proportional to $ \sqrt{V} $. Substituting into the radius formula, $ r \propto \sqrt{V} $, making option A correct. Students must understand the relation between kinetic energy and velocity in electromagnetic interactions.