# Magnetic field of parallel plates

1. Jul 29, 2011

### 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 text books...

Thanks to anyone who helps me try to get it!

2. Jul 29, 2011

### Drakkith

Staff Emeritus
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.

3. Jul 29, 2011

### sciillit

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?

4. Jul 29, 2011

### 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.