Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity v in a magnetic field B  . Show that no work is done by this force on the charged particle.

OR 

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.

Lorentz magnetic force is given by, 

Therefore, work done is, 

As, 

So, Work done, W = 0
                                                            OR

Consider two long straight conductors PQ and RS placed parallel to each other carrying currents I₁ and I₂ respectively. Conductors experience an attractive force when the conductors move in the same direction while, repulsive force is experienced by the conductors when currents move in opposite direction.

PQ and RS which are placed at a distance r, carry currents I₁ and I₂ in the same direction.
Suppose, a current element ‘ab’ of length  of wire RS.

The magnetic field produced by current-carrying conductor PQ at the location of other wire RS,

So, total force on the conductor of length L is given by, 

Force acting per unit length of conductor is given by,