Exemplar Problemsr

Problem 1 : Three point charges Q1, Q2, and Q3 are placed at the vertices of an equilateral triangle of side ‘a.’ Calculate the net electrostatic force on Q1 due to Q2 and Q3.

Solution : Let’s denote the charges and positions as follows:

• Q1 is at the origin (0, 0).
• Q2 is at (-a/2, a√3/2) because it’s one side of the equilateral triangle.
• Q3 is at (a/2, a√3/2) for the same reason.

The force on Q1 due to Q2 is given by Coulomb’s law: $$F_1 = \frac{k * |Q1 * Q2|}{r_{12}^2}$$

Similarly, the force on Q1 due to Q3 is: $$F_2 = \frac{k * |Q1 * Q3|}{r_{13}^2}$$

Here, $$r_{12}$$ and $$r_{13}$$ are the distances between charges Q1 and Q2, and Q1 and Q3, respectively.

Now, apply the superposition principle to find the net force on Q1: $$F_net = F_1 + F_2$$

Plug in the values and calculate.