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The wires which connect the battery of an automobile to its starting motor carry a current of $300 \mathrm{~A}$ (for a short time). What is the force per unit length between the wires if they are $70 \mathrm{~cm}$ long and $1.5 \mathrm{~cm}$ apart? Is the force attractive or repulsive?
The wires which connect the battery of an automobile to its starting motor carry a current of $300 \mathrm{~A}$ (for a short time). What is the force per unit length between the wires if they are $70 \mathrm{~cm}$ long and $1.5 \mathrm{~cm}$ apart? Is the force attractive or repulsive?
CBSE | Class 12 | Moving Charges and Magnetism | NCERT | NCERT | Physics
The wires which connect the battery of an automobile to its starting motor carry a current of $300 \mathrm{~A}$ (for a short time). What is the force per unit length between the wires if they are $70 \mathrm{~cm}$ long and $1.5 \mathrm{~cm}$ apart? Is the force attractive or repulsive?

Current flowing in the wires, $\mid=300 \mathrm{~A}$

Wires are separated by distance, $d=1.5 \mathrm{~cm}=0.015 \mathrm{~m}$

Length of the wires, $\mid=70 \mathrm{~cm}=0.7 \mathrm{~m}$

Force between the two wires, $F=\left.\mu_{0}\right|^{2} / 2 \pi d$

Here,

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

$F=\frac{4 \pi \times 10^{-7} \times(300)^{2}}{2 \pi \times 0.015}=1.2 \mathrm{~N} / \mathrm{m}$

Because the wires’ directions are opposing, the force will be repelling.

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