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 .

 

[Nickie]

I would like to clarify that the work done by the magnetic field is not always zero. The work done by the magnetic force is indeed zero, as the magnetic force is always perpendicular to the displacement of the charged particles and therefore does not do any work. However, in this scenario, the work is being done by an external agent, not just the magnetic force.

To answer the first question, the work done by the external agent would be equal to the change in potential energy of the system. This can be calculated by considering the gravitational potential energy of the raised wire B as well as the change in magnetic potential energy between the two wires. The total work done would be the sum of these two energies.

To answer the second question, the work done by the magnetic field itself (not the external agent) would be zero, as stated earlier. However, the work done by the external agent would not be zero, as there is a change in potential energy in the system. Therefore, the book is correct in stating that the work done is non-zero.

I hope this clarifies any confusion regarding the work done by the magnetic field in this scenario. It is important to differentiate between the work done by the magnetic force and the work done by an external agent in a system involving magnetic fields.