Question

The wires which connect the battery of an automobile to its starting motor carry a current of `300A` (for a short time). What is the force per unit length between the wires if they are `70cm` long and `1*5cm` apart? Is the force attractive or repulsive?

Answer 1

Current in both wires, `I = 300A`
Distance between the wires, `r = 1.5 cm = 0.015m`
Length of the wires, `l = 70 cm = 0.7m`
Force between the two wires is given by the relation,
`F = (mu_(0)I^(2))/(2pir)`
Where,
`mu_(0)=` Permeability of free space `= 4pi xx 10^(-7)TmA^(-1)`
`:. F = (4pi xx 10^(-7) xx (300)^(2))/(2pi xx 0.015)`
`=1.2 N//m`
Since the direction of the circuit in the wires is opposite, a repulsive force exists between them.