Wires A, B, C are three parallel current-carrying wires as...

Wires $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are three parallel current-carrying wires as shown in the diagram below; the wires are all $3.3 \mathrm{~m}$ long and $1.0 \mathrm{~m}$ apart from each other.
Determine the resultant force acting on wire $B$.

Key Concepts

Magnetic Field due to a Long Straight Conductor

This concept refers to the magnetic field generated by a steady electric current flowing through a long, straight conductor. The magnitude of the field decreases inversely with the distance from the wire, and its direction is determined using the right-hand rule. The mathematical expression commonly used is B = (??I)/(2?r), where ?? is the permeability of free space, I is the current, and r is the distance from the wire.

Lorentz Force on a Current-Carrying Conductor

The Lorentz force describes how a current-carrying conductor experiences a force when placed in an external magnetic field. The force is given by F = I L × B, where I is the current, L is the length vector of the conductor, and B is the magnetic field. The direction of this force is perpendicular to both the current direction and the magnetic field, as determined by the right-hand rule.

Superposition Principle in Electromagnetism

This principle states that when multiple magnetic fields are present, the resulting magnetic field at any point is the vector sum of the individual fields produced by each source. This concept is crucial when analyzing systems with several current-carrying wires, as the net force on a specific wire is computed by considering the individual forces due to each of the other wires.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor and the direction of the force on a moving charge or current in a magnetic field. By orienting the hand with the thumb pointing in the direction of the current or velocity, the curled fingers indicate the direction of the magnetic field encircling the conductor.

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