# The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time).

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? Is the force attractive or repulsive?

Solution:

Current in both wires, I = 300 A

Distance between the wires, = 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,

$F=\frac{\mu_{0} I^{2}}{2 \pi r}$

Where,

$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$

$\therefore F=\frac{4 \pi \times 10^{-7} \times(300)^{2}}{2 \pi \times 0.015}$

$=1.2 \mathrm{~N} / \mathrm{m}$

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