Question

Three charges, + 43 uC, - 43 uC and + 43 uC are placed at A (0,5cm), B (5cm,0), C(-5cm,0). Calculate the potential energy of the whole system of charges.

Answer 1

From the given (x,y) coordinates, It is very clear that the charges are arranged in a triangle with vertices at +5 on y-axis, + 5 on x axis and -5 on x axis. PLEASE NOTE THAT YOU HAVE NOT TOLD HOW THESE CHARGES ARE ARRANGED. I ASSUME THEY ARE ARRANGED RESPECTIVELY AS TOLD IN THE QUESTION. ANYWAY, THE METHOD WILL ALWAYS BE THE SAME. EVEN IF YOU WANT TO DO IT FOR DIFFERENT ARRANGEMENT, YOU CAN EASILY DO IT FOLLOWING THE METHOD I HAVE USED. YES, THE ANSWER WILL CHANGE IF WE CHANGE THE ARRANGEMENT. FOR EXAMPLE IF -43 uC CHARGE is at (0,5) then we will have

U = -235.37 + 166.41 - 235.37

U = kq₁q₂ / r

so, we have

U₁ = K(43E-6)(-43E-6) / 0.0707

U₁ = - 235.37

U₂ = K(-43E-6)(43E-6) / 0.1

U₂ = -166.41

U₃ = K(43E-6)(43E-6) / 0.0707

U₃ = 235.37

U = U₁ + U₂ + U₃

U = -235.37 - 166.41 + 235.37

U = -166.41