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?
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?
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,
$F=\frac{\mu_{0} I^{2}}{2 \pi r}$
Where, $\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \,T\,m\, A ^{-1}$
$\therefore F=\frac{4 \pi \times 10^{-7} \times(300)^{2}}{2 \pi \times 0.015}$
$=1.2 \,N / m$
since the direction of the current in the wires is opposite, a repulsive force exists between them.
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