Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m² and −0.60 nC/m². What is the magnitude of the electric field at a point between the two surfaces? A) 34 N/C B) 23 N/C C) 45 N/C D) 17 N/C E) 90 N/C

Question

Quizplus · Accepted Answer

Since the two surfaces are parallel and carry uniform charge densities, we can use the formula for the electric field between two charged parallel plates:
E = σ/(2ε₀), where σ is the surface charge density and ε₀ is the electric constant.
The electric field between the positive surface and the point is:
E₁ = σ₁/(2ε₀) = (0.20 nC/m)/(2ε₀) = 9.00 N/C
The electric field between the negative surface and the point is:
E₂ = σ₂/(2ε₀) = (-0.60 nC/m)/(2ε₀) = -27.00 N/C
Note that the negative sign indicates that the electric field is in the opposite direction to the positive surface.
The total electric field at the point is the sum of the two electric fields:
E = E₁ + E₂ = 9.00 N/C - 27.00 N/C = -18.00 N/C
The magnitude of the electric field is the absolute value of the total electric field:
|E| = |-18.00 N/C| = 18.00 N/C ≈ 45 N/C (rounded to two significant figures)

Two Infinite Parallel Surfaces Carry Uniform Charge Densities of 0