Question

6. Two long parallel wires carrying equal amount of currents in same directions and placed 1m away attract each other with a force of 2 × 10-7 N per meter of their lengths, then current in each wire will be: (a) 0 A (b) 1A (c) 2A (d) 3A​

Answer 1

Given info : two long parallel wires carrying equal amount of currents in same directions and placed 1 m away attract each other with a force of 2 × 10⁻⁷ N/m of their lengths.

To find : the current in each wire will be ...

solution :  if two long parallel wires carrying currents in the same directions and placed d distance, the force acting on each wire is given by, F = μ₀i₁i₂l/2πd

here, i₁ = i₂ = i (let)

distance between them, d = 1m

force per unit length , F/l = 2 × 10⁻⁷ N/m

permeability of medium, μ₀ = 4π × 10⁻⁷ N/A²

now, F/l = μ₀i₁i₂/2πd

⇒ 2 × 10⁻⁷ N/m =  4π × 10⁻⁷ N/A² × i²/(2π × 1)

⇒ i = 1A

therefore the current in each wire is 1 A.