Question

Two long straight thin wires AB and CD have linear charge densities 10 μC/m and −20 μC/m, respectively. They are kept parallel to each other at a distance 1 m. Find magnitude and direction of the net electric field at a point midway between them.

Answer 1

Given, λ₁ = 10 µC/m

λ₂ = −20 μC/m

d = 1 m

For a point at a distance from linear charge,

`E = lambda/(2 pi epsilon_0 r)`

Total electric field,

E = E₁ + E₂

`E = lambda_1/(2 pi epsilon_0 r) + lambda_2/(2 pi epsilon_0 r)`

`E = 2/(4 pi epsilon_0 r)(lambda_1 + lambda_2)`

`E = (2 xx 10^9 xx 9)/0.5 (10 xx 10^-6 - 20 xx 10^-6)`

E = −36 × 10⁹ × 10⁻⁵

E = −3.6 × 10⁵ N/C

The direction of the electric field is towards wire CD.