Two thin long parallel wires separated by a distance y are carrying a current I Amp each. The ma

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

Two thin long parallel wires separated by a distance $\mathrm{y}$ are carrying a current I Amp each. The magnitude of the force per unit length exerted by one wire on other is (a) $\left[\left(\mu_{0} I^{2}\right) / y^{2}\right]$ (b) $\left[\left(\mu_{o} I^{2}\right) /(2 \pi \mathrm{y})\right]$ (c) $\left[\left(\mu_{0}\right) /(2 \pi)\right](1 / y)$ (d) $\left[\left(\mu_{0}\right) /(2 \pi)\right]\left(1 / \mathrm{y}^{2}\right)$

Two thin long parallel wires separated by a distance $\mathrm{y}$ are carrying a current I Amp each. The magnitude of the force per unit length exerted by one wire on other is
(a) $\left[\left(\mu_{0} I^{2}\right) / y^{2}\right]$
(b) $\left[\left(\mu_{o} I^{2}\right) /(2 \pi \mathrm{y})\right]$
(c) $\left[\left(\mu_{0}\right) /(2 \pi)\right](1 / y)$
(d) $\left[\left(\mu_{0}\right) /(2 \pi)\right]\left(1 / \mathrm{y}^{2}\right)$

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Key Concepts

Magnetic Field due to a Current-Carrying Wire

A long straight current carrying conductor produces a magnetic field that circles the wire. The magnitude of this field at a distance y from the wire is given by B = (?? I)/(2? y), demonstrating how the field decreases with distance from the wire.

Magnetic Force between Parallel Currents

When two parallel wires carry currents, each wire experiences a magnetic field due to the other wire, resulting in a force per unit length. This force is given by F/L = I B, where B is the magnetic field from the other wire. This concept underpins how magnetic interactions can lead to attractive or repulsive forces between current elements.

Ampere's Law

Ampere's Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It is used to derive the expression for the magnetic field generated by current-carrying conductors, particularly in highly symmetric situations like an infinitely long straight wire.

Permeability of Free Space

The permeability of free space, ??, is a physical constant that relates magnetic field and magnetic flux in a vacuum. It appears in the formulas for the magnetic field due to a current and the magnetic force between currents, linking theoretical expressions with measurable quantities.

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