Magnetic field of parallel plates

[Notsureigetit]

Apologies if this has been answered before. I did search but couldn't find it...

Imagine two fixed conducting parallel plates separated by 10cm of air. If an alternating voltage is applied to these at 10MHz an electric field produced between the two plates like a giant capacitor. Given that this is a time varying field is a magnetic field also produced?

A supplementary question is whether or not you ave to have a loop to generate a magnetic field? - it is the example always shown in textbooks...

Thanks to anyone who helps me try to get it!

 

[Drakkith]

I believe this effect is exactly like two wires parallel to each other with an AC voltage applied. There is a magnetic field induced by the changing electric field I know that.

 

[sciillit]

Apologies if this has been answered before. I did search but couldn't find it...

Imagine two fixed conducting parallel plates separated by 10cm of air. If an alternating voltage is applied to these at 10MHz an electric field produced between the two plates like a giant capacitor. Given that this is a time varying field is a magnetic field also produced?

A supplementary question is whether or not you ave to have a loop to generate a magnetic field? - it is the example always shown in textbooks...

Thanks to anyone who helps me try to get it!

Eddy currents in the plates will produce a magnetic field. In a perfect capacitor no electrons will flow across the gap. But there will be electrons moving in a real capacitor across the gap, especially above dielectric breakdown voltages. Any accelerating electron will produce an EM field.

You do not need a loop to produce a magnetic, as an examination of the Biot Savart law will show you. For instance analyze an infinite current carrying wire.

But, is this practical in practice? Where do we find infinite current carrying wires in nature?

Imagine an electron emitted from a metal surface, and during flight it encounters a potential, or a force (or even a medium) that causes the particle to accelerate, before finally moving off a distance to possibly be re-absorbed.

The electron under acceleration produces a magnetic field, but is the electron in a closed loop?

 

[entphy]

Setting up an alternating electric field across the parrellel plate conductors should create an associated magnetic field as a result. The reason is the electric field in between the plates will be changing and so will be the associated electric flux emanating from the +ve charged electrode to the -ve charged electrode. Time changing electric flux is equivalent to current, even without physical electron or charge carriers moving through the space. By the modified(enhanced version) Ampere's Law in the Maxwell equation, the curl of the magnetic field strength is equal to the total contribution of the current density and the time derivative of the electric flux. Even if there is no dielectric breakdown to conduct charge carriers, the time varying electric flux set up as a result of the electric field between the plates would induce magnetic fields.

 

[sardar]

Yes, a magnetic field is also produced in this scenario. Whenever there is a time-varying electric field, a magnetic field is also generated according to Maxwell's equations. In this case, the alternating voltage at 10MHz will create an alternating electric field between the two parallel plates, which in turn will generate a magnetic field perpendicular to the electric field and parallel to the plates.

To answer the supplementary question, no, you do not always need a loop to generate a magnetic field. In this case, the plates themselves act as a loop since they are connected by the alternating voltage source. However, in most textbook examples, a loop is used to demonstrate the concept of a magnetic field because it allows for a more visual representation and easier calculations. But in reality, any time-varying electric field will produce a magnetic field, regardless of whether or not there is a loop present.