Yes, there is a magnetic field in the capacitor when an AC current flows through it . This magnetic field increases from the center of the capacitor to a maximum value at the edges of the capacitor and then decreases as we move away from the capacitor.
The magnitude of the magnetic field inside the capacitor is just B=ir/(2ϵ0c2 S) since r=(y2+z2)1/2 in Figure 17.2. p>
A capacitor stores potential energy in its electric field. This energy is proportional to both the charge on the plates and the voltage between the plates: UE = 1/2 QV. This expression can be combined with the definition of capacitance to get energy in terms of Q and C or Q and V.
Outside the capacitor the magnetic field has the same shape as that of a wire carrying the current I.
In a parallel plate capacitor a voltage applied between two conductive plates creates a uniform electric field between the plates. The electric field strength in a capacitor is inversely proportional to the distance between the plates and directly proportional to the applied voltage.
Reflection symmetry tells us that the electric field through both sides of the box parallel to the plates must be equal. This electric field must be zero because the box contains no net charge.
The electric field due to a plate of the capacitor is independent of distance (its uniformity) unless it is infinite. So if the finite identical plates have a uniform charge density, the field should be 0 away from the edges outside the capacitor.
Capacitance depends on factors such as plate area, separation distance and separator permittivity. These are not normally affected by a magnetic field.
When we find the electric field between the plates of a parallel plate capacitor, we assume that the electric field from both plates is E=σ2ϵ0^n. and zero everywhere else. Here σ is the surface charge density on a single side of the plate, or Q/2A since half the charge is on each side.
The electric field outside the capacitor is zero.
An electric current creates a magnetic field. This is possible when an electric charge is in motion. When the electric charge is at rest, no magnetic field is generated.
We already know that stationary charges create an electric field that is proportional to the magnitude of the charge. The same principle can be applied here, moving charges create magnetic fields that are proportional to the current, and therefore a current-carrying conductor creates a magnetic effect around it.
Electrostatic potential energy is stored in the capacitor. It is therefore related to the charge and voltage between the plates of the capacitor.
Since we know that the electric field is zero outside, we conclude that for the electric field to be zero inside the plate, the charge density on the outer surface of the plate must be zero , which means that all the charge is on the inside of the plate.
Reason: The field outside the capacitor is ε0σ. (σ is the charge density)
A capacitor can be slowly charged to the required voltage and then quickly discharged to provide the required energy. It is even possible to charge multiple capacitors to a certain voltage and then discharge them in a way that takes more voltage (but not more energy) out of the system than is put into it.
The simplest design for a capacitor is a parallel plate consisting of two metal plates with a gap between them: electrons are placed on one plate (the negative plate), while an equal amount of electrons become removed from the other plate (the positive plate).