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 q_{1} = 2µC, q_{2} = 4µC, q_{3} = 3 μC. (see figure below)

By Coulomb law, the electrostatic force on q_{2} due to q_{1}
is

Similarly, force on q_{2} due to q_{3} 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!)

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