A parallel plate capacitor is a device that uses two metal plates with the same surface area as electrodes. One plate is positive and the other is negative when a power source is applied. The plates are separated by a gap filled with a dielectric material, which doesn't conduct electricity but can hold electrostatic charges without any energy loss. The dielectric material's molecules get an electric dipole moment when placed in an external electric field, which is called electric polarisation.

When connected to a power source, one plate becomes positively charged while the other becomes negatively charged. This happens because the positive pole pushes electrons to the opposite plate. The charges are stored within the plates due to the attraction between the positive and negative charges. The electric field lines are formed between the two plates, from the positive to the negative charges.

The polarisation of the dielectric material by the electric field increases the capacitor's surface charge proportionally to the electric field strength. The formula for this is k × E / Eo, where k is the dimensionless dielectric constant, E is the permittivity of the material, and Eo is the permittivity of vacuum. This process is similar to magnetisation, where a magnetic dipole is induced in a magnetic material when placed near a magnet.

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Parallel plate capacitor: Derivation

A parallel plate capacitor has two plates separated by a distance d and filled with air. The cross-sectional area of each plate. E σ/A, where σ is the surface density. If the potential difference between the plates is V, then the capacitance can be calculated byuting the equation for electric potential. The capacitance depends on the distance between the plates, and the charge stored is proportional to the surface area and inversely proportional to distance. The Coulomb force between charges decreases with distance, so the closer the plates, the greater the attraction force between the opposite charges, resulting in a greater capacitance. Similarly, the bigger the plates, the greater the charge storing capacity.

Parallel Plate Capacitor: Leakage currents

When a charge is supplied to each plate of a capacitor, the potential increases. However, since there is no perfect dielectric material, the charge can leak and cause the capacitor to discharge once it's disconnected from the circuit. The time a capacitor can hold a charge depends on the quality of the dielectric material.

Parallel plate capacitor: Electric field

When a voltage is applied between the two conductive plates of a parallel plate capacitor, a uniform electric field is created between the plates. However, the geometry of the plates causes the electric field lines at the edges of the parallel plates to bend slightly upward, which is known as the fringing or edge effect. The strength of the electric field in a capacitor is directly proportional to the applied voltage but inversely proportional to the distance between the plates.

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Usage of parallel plate capacitors

Given that the initial capacitance the parallel plate capacitor is 5 mF. Let the initial distance between the plates be d.

The capacitance of the parallel plate capacitor is given by:

C = εA/d

Where ε is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.

Now, if the distance between the plates is reduced to a third of the initial distance, then the new distance between the plates is d/3.

Also, the space between the plates has a dielectric constant of 7. Therefore, the permittivity of the space between the plates is ε' = 7ε.

The new capacitance of the parallel plate capacitor is given by:

C' = ε'A/(d/3)

Substituting the values, we get:

C' = (7ε)(A)/((d/3))

C' = 21εA/d

C' = 21C

Therefore, the capacitance of the parallel plate capacitor after the distance between the plates is reduced to a third of the initial distance and with the space between the plates having a dielectric constant of 7 is 21 times the initial capacitance, which is 105 mF.

A squared length capacitor is a capacitor that has the same width and length. Hence, its area can be calculated by the squared length.

The capacitance of the parallel plate capacitor is given by:

C = Q/V

Where Q is the charge stored in the capacitor and V is the potential difference between the plates.

Substituting the given values, we get:

C = (1.2 ⋅ 10^-9 C)/(0.5 V)

C = 2.4 ⋅ 10^-9 F

The capacitance of the parallel plate capacitor is 2.4 ⋅ 10^-9 F.

The capacitance of a parallel plate capacitor is also given by:

C = εA/d

Where ε is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.

Rearranging the equation, we get:

A = Cdε

Substituting the values, we get:

A = (2.4 ⋅ 10^-9 F)(8.85 ⋅ 10^-12 F/m)/(3 ⋅ 10^-3 m)

A = 6.72 ⋅ 10^-8 m^2

Therefore, the area of the parallel plate capacitor is 6.72 ⋅ 10^-8 m^2.

Parallel Plate Capacitor

What is A parallel plate capacitor? 

A parallel plate capacitor is a type of capacitor that is constructed by two parallel conducting plates and a dielectric material between them.  It can be used to store electrical energy and signal processing.

How can we increase the capacitance of a parallel plate capacitor?

We can increase the capacitance of a parallel plate capacitor by increasing the area of the plates or decreasing the distance between the plates.

How does a parallel plate capacitor store energy?

A parallel plate capacitor stores electrical charges when there is a voltage difference between the plates. Because there is a dielectric material between the plates, the electrical charges will be stored in the dielectric material.

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