The force existing between two infinite parallel conductors is inversely proportional to ________

Question

Examoogle · Accepted Answer

Option D: The distance between the two conductors

Explanation & Concepts:
The force per unit length between two infinitely long, straight, parallel current-carrying conductors in free space is governed by Ampere's Force Law. This force is directly proportional to the product of currents flowing through the conductors and inversely proportional to the distance separating them.

Working Principle: A current-carrying conductor generates a magnetic field around itself according to Ampere's Law. When a second parallel conductor carrying current is placed within this magnetic field, it experiences a Lorentz force. Depending on the relative directions of the currents, the interaction produces an attractive force (for parallel currents) or a repulsive force (for antiparallel currents).

Key Formulas: $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$ — Force per unit length between two parallel conductors in N/m; $\frac{F}{L} \propto \frac{1}{d}$ — Inverse relationship between force and separation distance

Key Points: Parallel currents in the same direction attract each other.; Antiparallel currents (opposite directions) repel each other.; The SI definition of the Ampere is based on this force formulation between conductors.

Applications: Definition of the standard SI unit of electric current (Ampere).; Calculation of mechanical stress and forces between busbars during high short-circuit currents in power systems.

Additional Info: Option A is incorrect because the ideal formula assumes thin filamentary conductors; radius is neglected unless internal field effects/proximity effects are considered.. Option B is incorrect because force is directly proportional to the current in either conductor.. Option C is incorrect because force is directly proportional to the product of currents ($I_1 I_2$), not inversely proportional.

Answer: D is correct — The force per unit length between two parallel current-carrying conductors is inversely proportional to the separation distance $d$ between them.

Exam Tip: Always remember: like currents attract, unlike currents repel—the opposite rule of electrostatic charges where like charges repel!

Examoogle · Answer

Option A: The radius of the conductors

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Option B: Current in one of the conductors

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Option C: The product of the current in the two conductors

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