Two long, straight conductors are separated by a distance of $4.0, cm$ . The currents in them are $10, A$ and $5, A$ , flowing in opposite directions. What is the magnitude of the force per unit length on each conductor?

medium 3 marks Class 12 · Physics · Moving Charges and Magnetism

Answer

2.5 \times 1 0^{- 4}, N/m

(repulsive)

The correct answer is $2.5 \times 1 0^{- 4}, N/m$ (repulsive) — Result: $\frac{F}{L} = 2 \times 1 0^{- 7} \times 1250 = 2.5 \times 1 0^{- 4}, N/m$

Step-by-step solution

Use the formula $\frac{F}{L} = \frac{μ _{0} I _{1} I _{2}}{2 π d}$ with $μ_{0} = 4 π \times 1 0^{- 7}, T\cdotm/A$
Compute $\frac{μ _{0}}{2 π} = 2 \times 1 0^{- 7}, T\cdotm/A$
Multiply by $I_{1} I_{2} / d = (10) (5) / (0.04) = 1250$
Result: $\frac{F}{L} = 2 \times 1 0^{- 7} \times 1250 = 2.5 \times 1 0^{- 4}, N/m$

Common mistake: Assuming currents in same direction or using wrong sign for

I_{1} I_{2}

Concept tested: Force between parallel currents

Published 13 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

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Two long, straight conductors are separated by a distance of 4.0,cm. The currents in them are 10,A and 5,A, flowing in opposite directions. What is the magnitude of the force per unit length on each conductor?

Step-by-step solution

Two long, straight conductors are separated by a distance of $4.0, cm$ . The currents in them are $10, A$ and $5, A$ , flowing in opposite directions. What is the magnitude of the force per unit length on each conductor?