Electrical energy stored in solenoid

[PhysForumID]

I have a solenoid which has a current passing through it which increases linearly with time. I have proved that the energy stored in the magnetic field is equal to the energy being pumped in according to the surface integral of the poynting vector. This implies the energy stored in the electric field is zero (according to poynting's theorem which states the energy change for an EM system is the energy pumped into the E and B fields minus the energy flowing out of the surface in the poynting vector).
Why is the energy stored in the electric field zero? My attempt was that in a static situation (constant current I), the energy is entirely in the magnetic field since there is no electric field, so if we take this linear increase in a quasi-static manner, then the energy stored in each quasi-static situation should be equivalent to the same static situation, so it wouldn't make sense if energy was stored in the E-field in one situation but not in the other.

 

[weejee]

Although there is no magnetic field in the final state, there is a nonzero induce magnetic field when you increase the electric field from zero to the desired value. I guess if you take into account this fact you will get a reasonable answer.

 

[PhysForumID]

In a solenoid there is always a magnetic field in the core. As you increase current, the magnetic field increases causing a changing electric field in the core too. Why is there no energy stored in this created electric field?

 

[AJ Bentley]

Electric and magnetic fields are not separate things. They are just math. models to help us describe the interaction between charges, moving (B field) and stationary (E field).

Remember from relativity that the concepts stationary and moving have no meaning.
One observer's B field is another observer's E field.

In fact, these ideas of B and E hark back to the concept of the aether and are are so unsatisfactory now that they are being slowly replaced by a better model (The vector and scalar potentials)

 

[sardar]

I can confirm that your reasoning is correct. In a static situation, the energy is entirely stored in the magnetic field since there is no electric field present. This is because in a solenoid, the magnetic field is created by the flow of current through the coil, while the electric field is essentially "cancelled out" due to the symmetry of the solenoid's structure.

In the case of a linearly increasing current, the energy stored in the magnetic field also increases linearly. This is because the magnetic field strength is directly proportional to the current passing through the solenoid. As the current increases, so does the magnetic field and therefore the energy stored in it.

On the other hand, the energy stored in the electric field remains zero because the electric field is still being cancelled out by the symmetry of the solenoid's structure. This means that the energy being pumped into the electric field is being immediately converted into the magnetic field, resulting in no net change in the energy stored in the electric field.

In summary, the energy stored in the electric field is zero in a solenoid due to the cancellation of the electric field by its own structure. This is consistent with Poynting's theorem, which states that the change in energy for an electromagnetic system is equal to the energy pumped into the electric and magnetic fields minus the energy flowing out of the surface in the Poynting vector.