Question

Two infinite linear charges are placed parallel to each other at a distance 0.1 m from each other. if the linear charge density on each is 5 c/m, then the force acting on a unit length of each linear charge will be

Answer 1

We know, electric field on infinite linear charge , E = λL/2π∈₀r
where λ is linear charge density , r is the radius of circular part of linear charge.

we have to find out Force per unit length
e.g., F/L = qE/L , [ ∵ F = qE ]
Now, Force per unit length = qλL/2π∈₀rL = qλ/2π∈₀r
Put λ = 5 μC/m , q = 5μC , r = 0.1
∴ force per unit length = 5 × 10⁻⁶ × 5 × 10⁻⁶/2 × 3.14 × 8.857 × 10⁻¹² × 0.1
= 25 /6.28 × 0.8857
= 4.494 N/m

Answer 2

Hello Dear.
Here is the answer.
The Electric field on infinite linear charge is given by the formula,
E = λL/2π∈₀r

Also, F/L = qE/L
   ⇒ F = qE

∴ Force per unit length = qλL/(2π∈₀rL)
    = qλ/(2π∈₀r)
Where,F = Force per unit lengthλ = linear charge density
= 5 μC/m.
= 5 × 10⁻⁶ C/m.
Charge (q) = 5 μC
 = 5 × 10⁻⁶ C.

Distance between the charges (r) = 0.1 m.
∈₀ = 8.857 × 10⁻¹².


Putting these values in the Formula,
F = (5 × 10⁻⁶ × 5 × 10⁻⁶) ÷ (2 × (22/7) × 8.857 × 10⁻¹² × 0.1)
  = (25 × 10⁻¹²) ÷ (44/7 × 8.857 × 10⁻¹³)
  = (25 × 10) ÷ (55.67)
  = 0.449 × 10
  = 4.49 N/m.


∴ Force per unit length of each linear charge is 4.49 N/m.


Hope it helps.