How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle as shown in figure?

Given:


Charge at 1 : q₁ = 4.0 × 10^-5 C
Charge at 2 : q₂ = 2.0 × 10^-5 C
Charge at 3 : q₃ = 3.0 × 10^-5 C
Let side of the equilateral triangle be L = 10 cm = 0.1 m
Formula used:
To assemble the charges at three vertices electric potential energy is required.
Thus, the work done in assembling these charges is equal to the total electric potential energy used.
W = U₁₂ +U₂₃ + U₃₁
Here, W is the work done.
U₁₂: Electric Potential energy due to charges at 1 and 2 having separation 0.1 m.
U₂₃ : Electric Potential energy due to charges at 2 and 3 having separation 0.1 m.
U₃₁: Electric Potential energy due to charges at 3 and 1 having separation 0.1 m.
Formula for Electric potential energy is:
Here, k is a constant and k= =9× 10⁹ Nm²C^-2 , q₁ and q₂ are point charges and r is the separation between them and U is the electric potential energy required to moves charges q₁ and q₂ apart.
Substituting,



Hence, 234 J of work is required for assembling the charges at the vertices of the equilateral triangle.