Question

Please show all work. I am struggling with these concepts

What is the potential at point P due to Q, and Q? How much work was done in assembling the charge configuration shown below.

Answer 1

V_p = electric potential at P

V₁ = electric potential by charge Q₁ at P

V₂ = electric potential by charge Q₂ at P

Q₁ = 5 x 10^-6 C , r₁ = 1.12 m

Q₂ = 8 x 10^-6 C , r₂ = 0.50 m

Electric potential at P is given as

V_p = V₁ + V₂

V_p = kQ₁/r₁ + k Q₂/r₂

V_p = (9 x 10⁹) (5 x 10^-6)/(1.12) + (9 x 10⁹) (8 x 10^-6)/(0.50)

V_p = 1.84 x 10⁵ volts

2)

Work done = electric potential energy of the system of charges

W = k Q₁ Q₃ /r₁ + k Q₂ Q₃/r₂ + k Q₁ Q₂/r

W = (9 x 10⁹) (5 x 10^-6) (- 3 x 10^-6)/(1.12) + (9 x 10⁹) (8 x 10^-6) (- 3 x 10^-6)/(0.50) + (9 x 10⁹) (5 x 10^-6) (8 x 10^-6)/(1)

W = - 0.193 J