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?

Question

Quizplus · Accepted Answer

The electric field between two infinite parallel plates with uniform charge densities can be found by using the formula:

E = σ/2ε0

where σ is the charge density (in C/m2), and ε0 is the permittivity of free space (8.85 × 10-12 C2/N∙m2).

Plugging in the given values:

For the top plate, σ = 0.20 nC/m2 = 0.20 × 10-9 C/m2.
For the bottom plate, σ = -0.60 nC/m2 = -0.60 × 10-9 C/m2. (Note the negative sign is due to the fact that the bottom plate has an opposite charge.)
The net charge density between the two plates is σnet = σtop + σbottom = -0.40 × 10-9 C/m2.
Substituting these values, we get:

E = σnet/2ε0 = (-0.40 × 10-9 C/m2) / (2 × 8.85 × 10-12 C2/N∙m2) = 45 N/C

Therefore, the magnitude of the electric field at a point between the two surfaces is 45 N/C. The answer is (C).

Two Infinite Parallel Surfaces Carry Uniform Charge Densities of 0