Two long, parallel wire are separated by a distance of 2.50 cm . The force per unit length that

step 1 Okay, this is question 2830. We have two long parallel wires that are separated by a distance of

Two long, parallel wire are separated by a distance of 2.50...

Two long, parallel wire are separated by a distance of $2.50 \mathrm{~cm} .$ The force per unit length that each wire exerts on the other is $4.00 \times 10^{-5} \mathrm{~N} / \mathrm{m},$ and the wires repel each other. The current in one wire is 0.600 A. (a) What is the current in the second wire? (b) Are the two currents in the same direction or in opposite directions?

Two long, parallel wire are separated by a distance of $2.50 \mathrm{~cm} .$ The force per unit length that each wire exerts on the other is $4.00 \times 10^{-5} \mathrm{~N} / \mathrm{m},$ and the wires repel each other. The current in one wire is 0.600 A. (a) What is the current in the second wire?
(b) Are the two currents in the same direction or in opposite directions?

Key Concepts

Ampere's Law

Ampere's Law relates the integrated magnetic field around a closed loop to the total electric current passing through that loop. It is a cornerstone in the study of electromagnetism, especially useful in scenarios involving long, straight conductors where the symmetry of the system simplifies the calculation of magnetic fields.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field created by a current and the direction of the force on a current-carrying conductor in a magnetic field. By aligning the thumb with the current direction, the curvature of the fingers indicates the circular direction of the magnetic field, which is essential in visualizing magnetic interactions.

Magnetic Field of a Current-Carrying Conductor

A current flowing through a long, straight conductor creates a magnetic field that circles around the wire. The magnitude of this field at a distance from the wire is determined by the Biot–Savart law, and its direction follows from the right-hand rule. This concept is fundamental for understanding how wires interact through their generated fields.

Magnetic Force Between Parallel Currents

When two current-carrying wires are placed parallel to each other, each wire experiences a force due to the magnetic field produced by the other. The force per unit length is given by the formula F/L = (?? I? I?)/(2?d), where ?? is the permeability of free space, I? and I? are the currents, and d is the separation between the wires. This principle explains whether the wires attract or repel, depending on the directions of the currents.

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