Question

What is the magnitude of the electric field at a point midway between a −5.6μC and a +5.8μC charge 9.0cm apart? Assume no other charges are nearby.

Express your answer using two significant figures.

Answer 1

d = distance between two charges = 9 cm = 0.09 m

r = distance of midpoint from each charge = d/2 = 0.09/2 = 0.045 m

Q₁ = magnitude of charge on left = 5.6 x 10^-6 C

Q₂ = magnitude of charge on right = 5.8 x 10^-6 C

E₁ = magnitude of electric field by charge Q₁ = k Q₁/r²

E₂ = magnitude of electric field by charge Q₂ = k Q₂/r²

from the diagram , the two electric fields are in same direction

E = E₁ + E₂

E = (k Q₁/r² ) + (k Q₂/r²)

E = k (Q₁ + Q₂)/r²

inserting the values

E = (9 x 10⁹) (( 5.6 x 10^-6) + (5.8 x 10^-6))/(0.045)²

E = 5.1 x 10⁷ N/C