Question

An infinitely long wire is stretched horizontally 4 metre above the surface of the earth. It carries a charge
1 micro coulomb per cm of its length. Calculate its electric field at a point on the earth's surface vertically below the wire.

Answer 1

The electric field at a point on the earth's surface vertically below the wire is 44.92 N/C.

Explanation:

The electric field at the point vertically below the wire is given by the formula:

E = λ/(2πε₀R)

Where,

λ = Charge per unit length = 1μ C/cm = 1 × 10⁻⁶ × 10⁻² C/m

R = Distance between the point and the wire = 4 m

ε₀ = Permittivity of free space = 8.854 × 10⁻¹² F/m

On substituting the values, we get,

E = (1 × 10⁻⁶ × 10⁻²)/(2 × 22/7 × 8.854 × 10⁻¹² × 4)

E = (1 × 10⁻⁸)/(222.61 × 10⁻¹²)

∴ E = 44.92 N/C