Question

The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? 

Answer 1

Current in both wires, I = 300 A

Distance between the wires, r = 1.5 cm = 0.015 m

Length of the two wires, l = 70 cm = 0.7 m

Force between the two wires is given by the relation,

F = `(μ_0"I"^2)/(2π"r")`

Where,

μ₀ = Permeability of free space = 4π × 10⁻⁷ T mA⁻¹

∴ F = `(4π xx 10^-7 xx (300)^2)/(2π xx 0.015)`

= 1.2 N/m

Since the direction of the current in the wires is opposite, a repulsive force exists between them.