The distance between two thin long straight parallel...

The distance between two thin long straight parallel conducting wires is $b$. On passing the same current $i$ in them, the force per unit length between them will be
(A) Zero
(B) $\frac{\mu_{0} i^{2}}{2 \pi b}$
(C) $\frac{\mu_{0} i}{2 \pi b}$
(D) $\frac{\mu_{0} i}{2 \pi}$

Key Concepts

Magnetic Field of a Current-Carrying Conductor

A long straight conductor carrying an electric current produces a magnetic field that circles the conductor. The magnitude of the magnetic field at a distance from the wire is given by a formula derived using the Biot-Savart law, which shows that the field decreases inversely with the distance from the wire. This concept is fundamental for understanding the interaction between current-carrying conductors.

Lorentz Force on a Current Element

When a current-carrying conductor is placed in an external magnetic field, it experiences a force known as the Lorentz force. The force per unit length on the conductor depends on the current, the magnetic field strength, and the angle between the current direction and the magnetic field. This principle explains how magnetic fields can exert mechanical forces on currents.

Mutual Force between Parallel Currents

Two parallel conductors carrying currents exert forces on each other due to the magnetic fields they produce. According to Ampere's force law, the magnitude of the force per unit length between the wires depends on the current in the wires and the distance separating them. When the currents are in the same direction, the wires attract, and if they are in opposite directions, they repel. This mutual interaction is a classical demonstration of the relationship between electricity and magnetism.

Transcript

Please give Ace some feedback