Question

A +50 μC point charge is placed 48 cm from an identical +50 μC charge.

Part A

How much work would be required for an external force to move a +0.70 μC test charge from a point midway between them to a point 13 cm closer to either of the charges?

Express your answer using two significant figure

Answer 1

Q = 50 x 10^-6 C

r = distance between two charges = 48 cm = 0.48 m

V₁ = electric potential at midpoint between the two charge = 2 k Q/(r/2) = 2 (9 x 10⁹) (50 x 10^-6) /(0.48/2)

V₁ = 3.75 x 10⁶ volts

V₂ = electric potential at point 13 cm from midpoint

V₂ = k Q/(r/2 + 0.13) + k Q/(r/2 - 0.13)

V₂ = (9 x 10⁹) (50 x 10^-6) /(0.24 + 0.13) + (9 x 10⁹) (50 x 10^-6) /(0.24 - 0.13)= 5.31 x 10⁶ volts

$\Delta$V = V₂ - V₁ = (5.31 x 10⁶ ) - (3.75 x 10⁶) = 1.56 x 10⁶ volts

Q' = charge moved = 0.70 x 10^-6

W = work done = Q' $\Delta$V = (0.70 x 10^-6) (1.56 x 10⁶) = 1.1 J