Properties of Charges: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Properties of Charges. Understanding the underlying formula is key to arriving at the correct answer below:

The relativistic formula for mass,

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

accounts for how mass increases with velocity. This behavior arises because mass is a form of energy, and energy is affected by motion under relativity.

However, electric charge (

$q$

) is invariant under relativistic mechanics. Charge does not depend on the velocity of the particle. It remains constant in all inertial reference frames, which is a fundamental principle in physics.

Thus, the equivalent relation for electric charge is simply:

$$q = q_0$$

This reflects the fact that charge does not vary with velocity, unlike mass.