Problem 2: Charges 2µC, 3µC and 4µC are place in air at the vertices of an equilateral triangle of sides 10 cm. What is the magnitude of the resultant force acting on the 4µC charge?

Solution

We calculate the individual forces due to the remaining two charges and then find the vector sum of them.

So let q₁ = 2µC, q₂ = 4µC, q₃ = 3 μC. (see figure below)

By Coulomb law, the electrostatic force on q₂ due to q₁ is

Similarly, force on q₂ due to q₃ is

To find the resultant of these forces, we add the x and y-components of these forces (remember the angles are 60° each).

Magnitude of the resultant force is given by,

And

Magnitude of the resultant force is given by

Direction of the resultant force can be calculated by

Therefore, θ = 83°

(Note: When you change the vertices of 2µC and 3µC charges, it will affect the direction of the resultant force, too. Change these vertices and solve the problem yourselves!)