Question

Two large parallel conducting plates carry charges of equal magnitude and opposite charge. When you place a point charge q = +3.60 nC between the plates, the force on the point charge is 22.0 μN. What is the magnitude of the surface charge density on either plate? Express your answer with the appropriate units.

Answer 1

The magnitude of the surface charge density on either plate is approximately 5.41 × 10⁻⁸ C/(m²)

Step-by-step explanation:

The magnitude of the charge on each of the conducting plates = Equal

The orientation of the charges on each plate = Opposite charges

The magnitude of the point charge placed between the plates = +3.60 nC

The force acting on the point charge, q = 22.0 μN

Therefore, we have;

F = E × q

E = F/q = 22.0 μN/+3.60nC = 6,111.1111 V/m

We have;

`E = (\rho )/(\epsilon_0)`

Where;

ρ = The surface charge density

ε₀ = Absolute permittivity ≈ 8.85 × 10⁻¹² C²/(N·m²)

Therefore, we have;

ρ = E × ε₀ = 6,111.1111 V/m × 8.85 × 10⁻¹² C²/(N·m²) = 5.40833332 × 10⁻⁸ C/(m²)

∴ The magnitude of the surface charge density on either plate, ρ ≈ 5.41 × 10⁻⁸ C/(m²).