# Magnetic field and displacement current

• crx
In summary: From Maxwells equations,Curl H = sigma E + e e0 dE/dt = e e0/d dV/dt,so a varying voltage across the capacitor creates a magnetic field, even when the conductivity sigma = 0.
crx
Is there really a magnetic field around a capacitors (parallel plate) in vacuum dielectric fed by a variable voltage? Is there an experiment that can prove that we don't need actually a moving electrical charge to create a magnetic field, but a variable electric field in vacuum its enough?

The relation between charge Q and voltage V on a capacitor C is
Q = CV
The derivative is
dQ/dt = I = C dV/dt

So it requires a current I to produce a variable voltage dV/dt on a capacitor. So there is a moving electrical charge around the capacitor.
Bob S

Here is an example of the displacement current creating a real current. Take an air capacitor C with gap d and area A. Put and maintain a voltage V on it. So the charge
Q = CV = e0AV/d.
Now insert a dielectric of relative permittivity e and thickness d and area A in the capacitor. Now
Q' = C'V
where C = ee0A/d
There is a current in the external circuit that increases the charge Q on the plates to maintain the voltage V on the capacitor.
Bob S

Bob S said:
Here is an example of the displacement current creating a real current. Take an air capacitor C with gap d and area A. Put and maintain a voltage V on it. So the charge
Q = CV = e0AV/d.
Now insert a dielectric of relative permittivity e and thickness d and area A in the capacitor. Now
Q' = C'V
where C = ee0A/d
There is a current in the external circuit that increases the charge Q on the plates to maintain the voltage V on the capacitor.
Bob S

Yes,but this is because of the dielectric molecules are shielding and weakening the electric field, so the capacitor will need more charges to reach the power supply voltage, so there will be a current in the external circuit.
What i would like to know is that if a plate capacitor with no dielectric in vacuum (with a pretty large gap ), connected to a AC supply, will have a magnetic field exactly in the area between the plates where there are no moving charges, but only variable electric field...

crx said:
Yes,but this is because of the dielectric molecules are shielding and weakening the electric field, so the capacitor will need more charges to reach the power supply voltage, so there will be a current in the external circuit.
What i would like to know is that if a plate capacitor with no dielectric in vacuum (with a pretty large gap ), connected to a AC supply, will have a magnetic field exactly in the area between the plates where there are no moving charges, but only variable electric field...
From Maxwells equations,
Curl H = sigma E + e e0 dE/dt = e e0/d dV/dt,
so a varying voltage across the capacitor creates a magnetic field, even when the conductivity sigma = 0.
Bob S

## 1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges and can exert a force on other moving charges.

## 2. How is a magnetic field produced?

A magnetic field is produced by electric currents, which are generated by moving charges. It can also be produced by permanent magnets or changing electric fields.

## 3. What is displacement current?

Displacement current is a concept in electromagnetism that describes the flow of electric charge that is not carried by actual moving particles, but by changing electric fields. It was introduced by James Clerk Maxwell to explain the behavior of electric currents in a vacuum.

## 4. How is displacement current related to magnetic fields?

According to Maxwell's equations, a changing electric field can produce a magnetic field, and vice versa. Displacement current is one of the sources of magnetic fields, along with actual electric currents.

## 5. What are the practical applications of magnetic fields and displacement current?

Magnetic fields and displacement current have numerous practical applications, including in generators and motors, magnetic levitation systems, particle accelerators, and medical imaging devices such as MRI machines.

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