Question

What is the magnitude of the electric field at a point midway between a −6.5μC and a +8.2μC charge 9.6cm apart? Assume no other charges are nearby.

Express your answer using two significant figures.

Answer 1

a = distance between the two charges = 9.6 cm = 0.096 m

r = distance of each charge from the midpoint = a/2 = 0.096/2 = 0.048 m

Q₁ = magnitude of first charge = 6.5 x 10^-6 C

Q₂ = magnitude of second charge = 8.2 x 10^-6 C

E₁ = electric field by charge Q₁

E₂ = electric field by charge Q₂

Electric field by charge Q₁ at the midpoint is given as

E₁ = k Q₁ /r² = (9 x 10⁹) (6.5 x 10^-6)/(0.048)² = 2.5 x 10⁷ N/C

Electric field by charge Q₂ at the midpoint is given as

E₂ = k Q₂ /r² = (9 x 10⁹) (8.2 x 10^-6)/(0.048)² = 3.2 x 10⁷ N/C

Net electric field at the midpoint is given as

E = E₁ + E₂ = (2.5 x 10⁷) + (3.2 x 10⁷)

E = 5.7 x 10⁷ N/C