Two long straight wires are arranged parallel to each other and are kept $20$ cm apart in vacuum. They carry currents of $2$ A and $4$ A respectively in the same direction. What will be the magnetic force on a length of $10$ cm of either wire?
( $μ_{0} = 4 π \times 1 0^{- 7}$ SI units)

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TestHub · Accepted Answer

The magnetic force on a length L of either wire is given by the formula: F = 2 π d μ 0 ​ I 1 ​ I 2 ​ L ​ Given: I 1 ​ = 2 A I 2 ​ = 4 A d = 20 cm = 0.2 m L = 10 cm = 0.1 m μ 0 ​ = 4 π × 1 0 − 7 T m/A Substituting the values: F = 2 π × 0.2 4 π × 1 0 − 7 × 2 × 4 × 0.1 ​ F = 2 × 1 0 − 7 × 0.2 0.8 ​ F = 8 × 1 0 − 7 N Answer: 8 × 1 0 − 7 N

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