Question

A steady current (I₁) flows through a long straight wire. Another wire carrying steady current (I₂) in the same direction is kept close and parallel to the first wire. Show with the help of a diagram how the magnetic field due to the current I₁ exerts a magnetic force on the second wire. Write the expression for this force.

Answer 1

Magnetic field `vecB` will be moving into the page and I₂ is moving upward on the plane of the page.

Hence,

For a length L of the wire carrying the current I₂,

The force can be expressed as

`F_(21) = I_2LB_1`

    =`(mu_0I_1I_2)/(2pid)  L`

Where, d is the separation of the two wires. This force F₂₁ will be directed towards the wire I₁ from the wire I₂.