Two parallel wires in a horizontal plane carry currents I1...

Two parallel wires in a horizontal plane carry currents $I_{1}$ and $I_{2}$ to the right. The wires each have length $L$ and are separated by a distance $d$. (a) What are the magnitude and direction of the field due to wire 1 at the location of wire $2 ?$ (b) What are the magnitude and direction of the magnetic force on wire 2 due to this field? (c) What are the magnitude and direction of the field due to wire 2 at the location of wire $1 ?$ (d) What are the magnitude and direction of the magnetic force on wire 1 due to this field? (e) Do parallel currents in the same direction attract or repel? (f) What about parallel currents in opposite directions?

Key Concepts

Interaction between Parallel Currents

Parallel currents create magnetic fields that influence each other, leading to forces between the conductors. When the currents flow in the same direction, the wires experience an attractive force; when the currents are opposite, the wires repel each other. This phenomenon is central in the definition of the ampere and illustrates fundamental interactions in magnetostatics.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the orientation of vectors in electromagnetism. It is used to determine the direction of the magnetic field around a current-carrying conductor by pointing the thumb in the direction of the current and curling the fingers, which show the circular field direction. It is also used for finding the direction of the magnetic force on a current-carrying wire when the current and external magnetic field are known.

Magnetic Field of a Long Straight Conductor

A long straight conductor carrying an electric current produces a magnetic field that forms concentric circles around the wire. The magnitude of the field at any point is given by the expression B = ??I/(2?d), where ?? is the permeability of free space, I is the current, and d is the perpendicular distance from the wire. The field's direction is determined by the right-hand rule, which is a fundamental tool in electromagnetism.

Magnetic Force on a Current-Carrying Conductor

When a current-carrying conductor is placed in an external magnetic field, it experiences a force given by F = I(L × B), where L is the vector representing the length of the conductor and B is the magnetic field vector. This force arises from the interaction between the magnetic field created by one current and the current in the other conductor, and the direction of the force is found using the right-hand rule for cross-products.

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