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 Cages

• 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

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.