Question

Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in the figure. (Let x = 6.50 cm and y = 2.20 cm.)

Answer 1

a)

q₁ = 8 uC                  r₁ = x = 0.065

q₂ = 2 uC                 r₂ = sqrt(x² + y²) = sqrt(0.065² + 0.022²) = 0.069

q₃ = 4 uC                 r₂ = y = 0.022

Electric potential by the three other charges is given as

V = V₁ + V₂ + V₃

V = k q₁/r₁ + k q₂/r₂ + k q₃/r₃

V = (9 x 10⁹) ((8 x 10^-6)/0.065 + (2 x 10^-6)/0.069 + (4 x 10^-6)/0.022) = 3.01 x 10⁶ volts

b)

q₁ = 8 uC                  r₁ = x = 0.065

q₂ = - 2 uC                 r₂ = sqrt(x² + y²) = sqrt(0.065² + 0.022²) = 0.069

q₃ = 4 uC                 r₂ = y = 0.022

Electric potential by the three other charges is given as

V = V₁ + V₂ + V₃

V = k q₁/r₁ + k q₂/r₂ + k q₃/r₃

V = (9 x 10⁹) ((8 x 10^-6)/0.065 + (- 2 x 10^-6)/0.069 + (4 x 10^-6)/0.022) = 2.48 x 10⁶ volts