# Unit 2: Conductors, Capacitors, Dielectrics

## 2.1: Electrostatics with Conductors

### Electric Field on the Surface of a Conductor

• Electric field is a vector quantity that describes the force experienced by a charged particle in an electric field.

• Electric field lines are perpendicular to the surface of a conductor at every point on the surface.

• The electric field inside a conductor is zero, and any excess charge resides on the surface of the conductor.

• The electric field on the surface of a conductor is perpendicular to the surface and is proportional to the surface charge density.

• The electric field just outside the surface of a conductor is perpendicular to the surface and is equal to the electric field inside the conductor.

• The electric field just inside the surface of a conductor is perpendicular to the surface and is equal to the electric field outside the conductor.

• The electric field on the surface of a conductor is strongest where the surface is most curved, and weakest where the surface is most flat.

• The electric field on the surface of a conductor is affected by the presence of other charges and conductors in the vicinity.

### Electric Shielding

• Electric shielding: It is the process of reducing the electric field in a space by surrounding it with a conductive material.

• It is used to protect sensitive electronic equipment from electromagnetic interference (EMI) and radio frequency interference (RFI).

• Electric shielding can be achieved by using conductive coatings, conductive fabrics, or metal enclosures.

• The effectiveness of electric shielding depends on the conductivity of the material used, the thickness of the shielding, and the frequency of the electromagnetic waves.

• Faraday cage: It is a type of electric shielding that completely surrounds a space with a conductive material, creating a barrier that prevents electromagnetic waves from entering or leaving the space.

• These are used to protect sensitive electronic equipment from lightning strikes, electromagnetic pulses (EMPs), and other forms of electromagnetic interference.

• These can be made from a variety of materials, including copper, aluminum, and steel.

• The effectiveness of a Faraday cage depends on the conductivity of the material used, the thickness of the shielding, and the frequency of the electromagnetic waves.

• Faraday cages are commonly used in electronic devices such as cell phones, computers, and radios to prevent interference from external sources.

## 2.2: Capacitors

• Capacitor: An electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by a dielectric material.

• Capacitance: It is the ability of a capacitor to store charge.

• `C = Q/V`

• where

• C is capacitance

• Q is charge

• V is voltage.

### Charging and Discharging

• When a capacitor is connected to a voltage source, it charges up to the voltage of the source. The time it takes to charge depends on the capacitance and the resistance of the circuit.

• When a charged capacitor is disconnected from the voltage source, it discharges through the circuit. The time it takes to discharge depends on the capacitance and the resistance of the circuit.

### Parallel Plate Capacitor

• Parallel plate capacitor: It is a device that stores electrical energy in an electric field between two parallel conducting plates. It consists of two parallel plates separated by a dielectric material.

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

• `C = εA/d`

• where

• C is the capacitance

• ε is the permittivity of the dielectric material between the plates

• A is the area of each plate

• d is the distance between the plates.

• The electric field between the plates of a parallel plate capacitor is given by:

• `E = V/d`

• where:

• E is the electric field

• V is the potential difference between the plates

• d is the distance between the plates.

• The energy stored in a parallel plate capacitor is given by:

• `U = (1/2)CV^2`

• where:

• U is the energy stored

• C is the capacitance

• V is the potential difference between the plates.

### Types of Capacitors

• Ceramic capacitors: These are the most commonly used type of capacitor.

• They are made of ceramic materials and have a high dielectric constant.

• They are small in size and have a low cost.

• They are used in high-frequency applications, such as in filters and resonant circuits.

• Electrolytic capacitors: These are polarized capacitors that use an electrolyte as the dielectric.

• They have a high capacitance and are used in low-frequency applications, such as in power supplies and audio circuits.

• They are available in two types: aluminum electrolytic capacitors and tantalum electrolytic capacitors.

• Film capacitors: These are non-polarized capacitors that use a thin plastic film as the dielectric.

• They have a high stability and are used in high-frequency applications, such as in radio and television circuits. They are available in two types: polyester film capacitors and polypropylene film capacitors.

• Tantalum capacitors: These are polarized capacitors that use tantalum metal as the anode.

• They have a high capacitance and are used in low-frequency applications, such as in power supplies and audio circuits.

• They are smaller in size than aluminum electrolytic capacitors and have a longer lifespan.

• Variable capacitors: These are capacitors whose capacitance can be adjusted.

• They are used in tuning circuits, such as in radios and televisions.

• They are available in two types: air variable capacitors and trimmer capacitors.

### Energy in a Capacitor

• The energy stored in a capacitor can be calculated using the formula:

• `E = 1/2 * C * V^2`

• where:

• E is the energy stored in joules

• C is the capacitance of the capacitor in farads

• V is the voltage across the capacitor in volts.

• The energy stored in a capacitor is proportional to the square of the voltage across it.

• This means that if the voltage across a capacitor is doubled, the energy stored in it will be quadrupled.

• The energy stored in a capacitor can be used to do work.

• For example, a capacitor can be used to power a flash in a camera.

• When the flash is triggered, the energy stored in the capacitor is released, producing a bright flash of light.

• The energy stored in a capacitor can also be used to filter out unwanted frequencies in a circuit.

• Capacitors are often used in filters to remove noise from signals.

## 2.3: Dielectrics

• Dielectrics: These are materials that do not conduct electricity easily.

• They are used in capacitors to store electrical energy and in insulators to prevent electrical current from flowing.

• Polar dielectrics have a permanent dipole moment due to the presence of polar molecules.

• They align themselves in an electric field and increase the capacitance of the capacitor.

• Examples of polar dielectrics include water, mica, and ceramic.

• Non-polar dielectrics do not have a permanent dipole moment.

• They are made up of non-polar molecules and do not align themselves in an electric field.

• Examples of non-polar dielectrics include air, vacuum, and oil.

• Dielectric strength: It is the maximum electric field that a dielectric material can withstand before it breaks down and conducts electricity. It is measured in volts per meter (V/m). The dielectric strength of a material depends on its thickness, temperature, and the frequency of the electric field.

### Common Dielectrics

Material

Dielectric Constant (k)

Air

1.0006

Vacuum

1.0

Teflon

2.1 - 2.3

Glass

4.5 - 8.5

Water

80.4

Diamond

5.5

### Why Does Adding a Dielectric Increase the Capacitance?

• Polarization of Dielectric Material

• When a dielectric material is inserted between the plates of a capacitor, it gets polarized due to the electric field produced by the capacitor.

• The polarization of the dielectric material creates an additional electric field that opposes the electric field produced by the capacitor.

• This reduces the effective electric field between the plates of the capacitor, which in turn increases the capacitance of the capacitor.

• Increase in Electric Flux Density

• The electric flux density between the plates of a capacitor is directly proportional to the electric field produced by the capacitor.

• When a dielectric material is inserted between the plates of a capacitor, the electric flux density increases due to the polarization of the dielectric material. This increase in electric flux density leads to an increase in the capacitance of the capacitor.

• Reduction in Electric Field

• The electric field between the plates of a capacitor is reduced when a dielectric material is inserted between the plates.

• This is because the dielectric material reduces the potential difference between the plates of the capacitor.

• As a result, the electric field between the plates of the capacitor is reduced, which in turn increases the capacitance of the capacitor.