Question

Two thin long parallel wires separated by a distance y are carrying a current I Amp each. The magnitude of the force per unit length exerted by one wire on other is __________ 

(a) [(μoI²)/y²] 

(b) [(μoI²)/(2πy)] 

(c) [(μo)/(2π)](1/y) 

(d) [(μo)/(2π)] (1/y²)

Answer 1

The correct option (b) [(μ_oI²)/(2πy)]

Explanation:

For long parallel wires, F = (μ₀/2π) [(I₁I₂ℓ)/y]

Here I₁ = I₂ = I   hence   (F/ℓ) = (μ₀/2π)(I²/y)

i.e. Force per unit length = [(μ₀I²)/(2πy)]