Whenever two parallel conductors carry current in them, the force between the conductors is:

Concept:

• Ampere's Circuital Law: It states the relationship between the current and the magnetic field created by it.
• This law states that the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium.

From the Ampere’s circuital law, the magnitude of the field due to the first conductor can be given by,

Ba = μ0 I1 / 2 π r

The force on a segment of length L of the conductor 2 due to the conductor 1 can be given as,

F21 = I2 L B1 = μ0 I1 I2 L / 2πr

From the equation
\({{\rm{F}}_{21}} = \frac{{{{\rm{\mu }}_{0{\rm{\;}}}}{{\rm{I}}_1}{\rm{\;}}{{\rm{I}}_2}{\rm{\;L}}}}{{2{\rm{\;\pi \;r}}}}\)

F \(\propto \frac{I_1 I_2 L}{r}\)

Explanation:

From the above relation, the force between the conductors is

• proportional to the product of currents in the two conductors and also directly proportional to the length of the section considered
• inversely proportional to the distance of separation between the conductors.