Additivity of Charges

Concept: Charge Adds Like a Real Number

Charge is a scalar quantity — it has magnitude but no direction, just like mass.

However, unlike mass (which is always positive), charge can be positive or negative.

Therefore, when adding charges, we must use algebraic addition — including the correct sign.

The Rule of Additivity

If a system contains two point charges $q_1$ and $q_2$, the total charge $Q$ of the system is:

This is algebraic addition — if $q_1$ is positive and $q_2$ is negative, their signs are included.

For a system containing $n$ point charges $q_1, q_2, q_3, \dots, q_n$, the total charge is:

Why This Matters

• Charges add like real numbers — they are scalars.
• The sign of each charge must be used in the sum.
• This is different from mass, which is always positive.

Worked Example from the Textbook

A system contains five charges (in some arbitrary unit): …