Is Magnetic Field Work Always Zero in Current-Carrying Conductors?

[smatik]

Two straight current carrying conductors A and B are lying in a vertical plane as shown.The separation between them is h and mass per unit length of wires is λ.Keeping one wire fixed (say A),Bis raised by small hieght δh.
Q-1 What would be the work done by external agent?
Q-2 Will the work done by magnetic field zero?[Answer this question first. I m confused since i was told that the work done by magnetic force(just magnet force not Lorentz) is always zero.But the book says "Work done is non zero",i think the book's wrong]

 

[kushan]

The book is right work is being done as F.ds is working .
In the case you are talking about F.ds the angle is 90 degree that's why no work done.

 

[smatik]

is the work done by magnetic force always zero??

 

[kushan]

See , when magnetic force acts on a charge , it doesn't change its speed , it just gives it centripetal acceleration . And direction of force is always perpendicular to motion .
I can say when ever Force is acting perpendicular to the motion of the body , work done is zero .