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?
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,
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!)