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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 x 10 -6 C/m, then the force acting on a unit length of each linear charge will be :

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 x 10-6 C/m, then the force acting on a unit length of each linear charge will be :
 

Grade:12

1 Answers

Rudransh
12 Points
2 years ago
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

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