Force Acting on Moving Charges: Practice Problem & Solution
A beam of cathode rays is subjected to crossed Electric (E) and Magnetic field (B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by (where V is the potential difference between cathode and anode): (2010 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:
For undeflected motion, velocity is $v = \frac{E}{B}$.
Equating kinetic energy to electrical work gives $\frac{1}{2}mv^2 = eV$.
Substituting velocity yields specific charge $\frac{e}{m} = \frac{E^2}{2VB^2}$.
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