Two thin long parallel wires separated by a distance b are...

Two thin long parallel wires separated by a distance $b$ are carrying a current $I$ amp each. The magnitude of the force per unit length exerted by one wire on the other is : (a) $\frac{\mu_{0} I^{2}}{b^{2}}$ (b) $\frac{\mu_{0} l^{2}}{2 \pi b}$ (c) $\frac{\mu_{0} I}{2 \pi b}$ (d) $\frac{\mu_{0} l}{2 \pi b^{2}}$

Two thin long parallel wires separated by a distance $b$ are carrying a current $I$ amp each. The magnitude of the force per unit length exerted by one wire on the other is :
(a) $\frac{\mu_{0} I^{2}}{b^{2}}$
(b) $\frac{\mu_{0} l^{2}}{2 \pi b}$
(c) $\frac{\mu_{0} I}{2 \pi b}$
(d) $\frac{\mu_{0} l}{2 \pi b^{2}}$

Key Concepts

Magnetic Field from a Long Straight Conductor

This concept refers to the determination of the magnetic field created by a current-carrying conductor, where the field’s magnitude at a distance from the wire is given by the relation B = (??I)/(2?r). This formula is derived from Ampère's law and is crucial for understanding how currents produce magnetic fields in space.

Ampère's Law

Ampère's law is one of Maxwell's equations and relates the integrated magnetic field around a closed loop to the electric current passing through that loop. It is especially useful in calculating magnetic fields in scenarios with high symmetry, such as the field around a long, straight conductor.

Lorentz Force on a Current-Carrying Conductor

The Lorentz force law explains that a current-carrying conductor placed in a magnetic field experiences a force. This force per unit length can be expressed as F/L = I × B when the current and the magnetic field are perpendicular. This concept is fundamental in understanding how magnetic fields can exert mechanical forces on conductors.

Force Between Parallel Currents

When two parallel conductors carry currents, each produces a magnetic field that exerts a force on the other according to the Lorentz force law. The magnitude of the force per unit length between them is derived by first calculating the magnetic field due to one wire at the location of the other and then applying the Lorentz force law. This interaction is a key demonstration of the interplay between electricity and magnetism.

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