Question

Two infinite linear charges are placed parallel at 0.1 m apart. if each has charge density of 5m c/ m, then the force per unit length of one of linear charges in n/m is :​

Answer 1

Given , linear charge density , λ = 5mC/m = 5 × 10⁻³ C/m

Separation between two parallel line charge , r = 0.1 m

we know, Electric field intensity act at r distance from the infinite line charge , E = λ/2πε₀r = λL/2πε₀rL = q/(2πε₀rL)

Here , q = 5 × 10⁻³ C per unit length

now, force , F = qE = q²/2πε₀L

F/L = q²/2πε₀r

Force per unit length = q²/2πε₀r

Now, put q = 5 × 10⁻³ C , r= 0.1

Force per unit length = (5 × 10⁻³)²/2 × 3.14 × 8.854 × 10⁻¹² × 0.1 N/m

= 25 × 10⁶/6.28 × 0.8854 N/m

= 4.50 × 10⁶ N/m