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Two parallel long thin wires, each carrying current I, are kept at a separation r from each other. Hence the magnitude of force per unit length of one wire due to the other wire is ______.

Asked in GSEB Board March 2019 · Force between parallel currents

• (1) (μ₀I²)/(2π r)
• (2) (μ₀I²)/(2r)
• (3) (μ₀I)/(2π r)
• (4) (μ₀I)/(2π r²)

Step-by-step solution

Why the other options are wrong

• (2) The π has gone missing. μ₀ sits over 2π r, not over 2r, so this option is π times too large.
• (3) This is the field one wire makes at the other, B=(μ₀I)/(2π r), measured in tesla. The force per unit length is BI, so one factor of the current is missing.
• (4) Two things are wrong here: the force per unit length is quadratic in the current, and it falls as 1/r, not as 1/(r²) — a long straight wire is not a point source.

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