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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?
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Solution
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.
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