Question

a long solid rod 4.5 cm in radius carries a uniform volume charge density. if the electric field strength at the surface of the rod (not near either end) is 16 kn/c, what is the volume charge density

Answer 1

6.29 μC/m³

Step-by-step explanation:

Volume charge density is the quantity of charge per unit volume.

The direction of the electric field was not specified, therefore the volume charge density (ρ) is given by:

2πRLE = ρπR²L/ε₀

ρ = 2Eε₀ / R

Where E = electric field strength = 16 kN/C = 16 * 10³ N/C, R = radius of rod = 4.5 cm = 0.045 m, ε₀ = relative permittivity of free space = 8.85 * 10⁻¹² C² / Nm²

Therefore:

ρ = 2(16 * 10³ N/C)(8.85 * 10⁻¹² C²/Nm²) / 0.045 m = 6.29 * 10⁻⁶ C/m³

ρ = 6.29 μC/m³