Question

10. Consider the group of charges in this figure. All three charges have Q = 2.4 nC. what is their electric potential energy 3 cm 4 cm

can you explain in diagrams and very in depth? thank you.

Answer 1

Potential energy of the system is same as that of the work done to assemble all the charges.
Consider the charge at the bottom be A, charge at the top left be B and charge at the top right be C.
Consider r1 = 4 cm, r2 = 3 cm
r3 = SQRT[(4)² + (3)²] = SQRT[25]
= 5 cm

Consider that initially, there were no charges. Work done to bring charge A from infinity,
W1 = 0 since it doesn't have to do work against any other charge.

Now A is in its position. Next we bring the charge B. We need to do work against the repulsive force due to charge A.
W2 = Kq²/(r1)
Where K = 1/4$\dpi{100} \pi$$\dpi{100} \epsilon$o = 9 x 10⁹ Nm²/C².

When we bring charge C, we need to do work against both A and B.
W3 = Kq²/(r2) + Kq²/(r3)

Total work done = W1 + W2 + W3
= 0 + Kq²/(r1) + Kq²/(r2) + Kq²/(r3)
= Kq²[1/(0.04) + 1/(0.03) + 1/(0.05)]
= [9 x 10⁹ x (2.4 x 10^-9)²] x [78.33]
= 4.061 x 10^-6 J