. Two long current-carrying wires run parallel to each...

Name: Problem 54, Chapter 20: College Physics
Uploaded: 2019-06-01T05:45:09-08:00
Duration: 1 min 39 s
Channel: Averell Hause
Description: . Two long current-carrying wires run parallel to each other. Show that if the currents run in the same direction, these wires attract each other, whereas if they run in opposite directions, the wires repel.

. Two long current-carrying wires run parallel to each other. Show that if the currents run in the same direction, these wires attract each other, whereas if they run in opposite directions, the wires repel.

Key Concepts

Magnetic Field of a Current-Carrying Conductor

A current-carrying conductor produces a magnetic field in the surrounding space, which circulates around the wire. This is described by both the Biot-Savart Law and Ampere’s Law. The magnetic field's magnitude and direction depend on the current and the distance from the wire, creating the basis for understanding how conductors interact magnetically.

Lorentz Force

The Lorentz force is the force experienced by a current-carrying conductor when it is placed in a magnetic field. This force is given by the vector cross product of the current element and the magnetic field. It is this interaction that causes the attraction or repulsion between wires depending on the relative directions of their currents.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current or the direction of the force on a current-carrying conductor in a magnetic field. By aligning the thumb with the direction of conventional current, the curled fingers point in the direction of the generated magnetic field, which is essential for visualizing and predicting the interactions between multiple conductors.

Interaction of Parallel Currents

The interaction of parallel currents is a direct outcome of the magnetic fields generated by each current-carrying wire and the forces that arise from those fields. When wires carry currents in the same direction, the resulting magnetic fields interact in such a way as to pull the wires toward each other, whereas opposite currents result in a repelling force. This fundamental concept underpins many applications in electromagnetism and electrical engineering.

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