Application of Maxwell's stress tensor to linear pull type solenoids

[dmorris619]

My professor recently tasked me with first understanding maxwell's stress tensor and then applying it to analyze the force produced by a linear pull type solenoid.

However after having studied the stress tensor I am not sure that I can apply the stress tensor to a solenoid. I don't believe that the electric force F = E*rho, where E is the electric field and rho is the charge density. In my understanding of how a solenoid operates the current flowing through the wires generates a Magnetic field, H, which in turn magnetizes the plunger. The plunger then wants to minimize the current flowing through the wires so it moves in closing the air gap. So the force generated is purely magnetic.

Am I right in thinking this or can maxwell's stress tensor be applied to it. Also if it cannot be applied to a solenoid can you give me an example of something it may be applied to?

 

[Vailanor]

Maxwell's stress tensor can be used to analyze the force produced by a linear pull type solenoid, though it may not be the most useful approach. The force produced by a solenoid is related to the Lorentz force, which is the force generated by a magnetic field on a moving charge. The Lorentz force is given by F = q*(v x B), where q is the charge of the particle, v is its velocity, and B is the magnetic field. This can be expressed in terms of Maxwell's stress tensor as F = -1/2 (E x H) where E is the electric field and H is the magnetic field. This tells us that the force produced by a solenoid is determined by both the electric and magnetic fields present in the system.