Learning Objectives

• Understand the concept of electric field and potential
• Learn about the calculations related to electric field and potential
• Understand the concept of capacitance
• Define capacitance and learn about its unit
• Learn about the parallel plate capacitor and its properties

Electric Field

• Electric field is the region around a charged object where the electric force acts on other charged objects.
• It is a vector quantity and is represented by the symbol E.
• The electric field at a point in space is defined as the force per unit positive charge experienced by a test charge placed at that point.

Electric Field Calculation

• Formula: Electric field strength, E = F/Q, where F is the force experienced by a test charge Q.
• Example:
  • If a point charge of +4 μC experiences an electric force of 6 N, calculate the electric field strength at the location of the point charge.
  • Given: Q = +4 μC, F = 6 N
  • Using the formula, E = F/Q = 6 N / (+4 μC) = 1.5 N/C

Electric Potential

• Electric potential is the amount of work done in bringing a unit positive charge from infinity to a specific point in an electric field.
• It is a scalar quantity and is represented by the symbol V.
• The SI unit of electric potential is the volt (V).

Electric Potential Calculation

• Formula: Electric potential, V = W/Q, where W is the work done in bringing the charge Q.
• Example:
  • If a positive charge of +2 μC requires 10 J of work to bring it from infinity to a point in an electric field, calculate the electric potential at that point.
  • Given: Q = +2 μC, W = 10 J
  • Using the formula, V = W/Q = 10 J / (+2 μC) = 5 V

Capacitance

• Capacitance is the ability of a body or system to store electrical energy in the form of an electric charge.
• It is defined as the ratio of the amount of charge stored on one of the conductors to the potential difference between them.
• The SI unit of capacitance is the farad (F).

Capacitance Calculation

• Formula: Capacitance, C = Q/V, where Q is the charge stored and V is the potential difference.
• Example:
  • A capacitor stores a charge of 4 μC when a potential difference of 2 V is applied across its plates. Calculate the capacitance of the capacitor.
  • Given: Q = 4 μC, V = 2 V
  • Using the formula, C = Q/V = 4 μC / 2 V = 2 μF

Parallel Plate Capacitor

• A parallel plate capacitor is a simple type of capacitor that consists of two parallel conducting plates separated by a dielectric material.
• The capacitance of a parallel plate capacitor depends on the area of the plates, the distance between them, and the dielectric constant of the material between the plates.
• It is commonly used in electronic circuits for energy storage and filtering.

Properties of Parallel Plate Capacitor

• The capacitance of a parallel plate capacitor is directly proportional to the area of the plates.
• The capacitance of a parallel plate capacitor is inversely proportional to the distance between the plates.
• The dielectric constant of the material between the plates affects the capacitance.

Example

• A parallel plate capacitor has an area of 0.5 m², a separation of 0.02 m, and a dielectric constant of 3. Calculate the capacitance of the capacitor.
• Given: A = 0.5 m², d = 0.02 m, κ = 3
• Using the formula, C = (κε₀A) / d = (3 * 8.85 x 10⁻¹² F/m * 0.5 m²) / 0.02 m = 0.6625 μF

Note: The remaining slides will be continued in the next set.

Electric Field and Potential - Continued

• The electric field and electric potential are related to each other.
• The electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point.
• Mathematically, it can be expressed as V = kQ/r, where k is the electrostatic constant, Q is the charge, and r is the distance from the charge.

Electric Potential Difference

• The electric potential difference, also known as voltage, is the change in electric potential between two points in an electric field.
• It is denoted by ∆V and is calculated using the formula ∆V = V₂ - V₁, where V₁ and V₂ are the electric potentials at the two points.

Capacitors in Series

• When capacitors are connected in series, the total capacitance is given by the reciprocal of the sum of the reciprocals of individual capacitances.
• Mathematically, for two capacitors C₁ and C₂ in series, the total capacitance Cₜ = 1/(1/C₁ + 1/C₂).

Capacitors in Parallel

• When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances.
• Mathematically, for two capacitors C₁ and C₂ in parallel, the total capacitance Cₜ = C₁ + C₂.

Energy Stored in a Capacitor

• The energy stored in a capacitor can be calculated using the formula E = 0.5 * C * V², where E is the energy, C is the capacitance, and V is the potential difference across the capacitor.
• The unit of energy is joules (J) and the unit of capacitance is farads (F).

Dielectric Material

• A dielectric material is an insulating material that is placed between the plates of a capacitor to increase the capacitance.
• It reduces the effective electric field between the plates and stores more charge for the same potential difference.
• Common dielectric materials include air, paper, mica, and various types of plastics.

Dielectric Constant

• The dielectric constant, also known as the relative permittivity, is a measure of how effectively a dielectric material stores electrical energy.
• It is represented by the symbol κ and is defined as the ratio of the electric field in a vacuum to the electric field in the dielectric material.
• The dielectric constant of a vacuum is 1.

Calculating Capacitance with Dielectric Material

• When a dielectric material is inserted between the plates of a capacitor, the capacitance increases by a factor of the dielectric constant.
• Mathematically, the new capacitance C’ = κ * C, where C is the original capacitance and κ is the dielectric constant.

Applications of Capacitors

• Capacitors are widely used in various electrical and electronic devices.
• They are used for energy storage, filtering, timing, voltage regulation, coupling, and decoupling in circuits.
• Capacitors are also used in power factor correction, motor starters, electronic oscillators, and radio frequency applications.

Summary

• Electric field and electric potential are important concepts in physics.
• Capacitance is the ability of a system to store electrical energy.
• Capacitors can be connected in series or parallel to modify the total capacitance.
• The energy stored in a capacitor can be calculated using the formula E = 0.5 * C * V².
• Dielectric materials increase the capacitance of a capacitor.
• Capacitors have various applications in electrical and electronic devices.

Electric Field and Potential - Continued

• The electric field and electric potential are related to each other.
• The electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point.
• Mathematically, it can be expressed as V = kQ/r, where k is the electrostatic constant, Q is the charge, and r is the distance from the charge.

Electric Potential Difference

• The electric potential difference, also known as voltage, is the change in electric potential between two points in an electric field.
• It is denoted by ∆V and is calculated using the formula ∆V = V₂ - V₁, where V₁ and V₂ are the electric potentials at the two points.

Capacitors in Series

• When capacitors are connected in series, the total capacitance is given by the reciprocal of the sum of the reciprocals of individual capacitances.
• Mathematically, for two capacitors C₁ and C₂ in series, the total capacitance Cₜ = 1/(1/C₁ + 1/C₂).

Capacitors in Parallel

• When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances.
• Mathematically, for two capacitors C₁ and C₂ in parallel, the total capacitance Cₜ = C₁ + C₂.

Energy Stored in a Capacitor

• The energy stored in a capacitor can be calculated using the formula E = 0.5 * C * V², where E is the energy, C is the capacitance, and V is the potential difference across the capacitor.
• The unit of energy is joules (J) and the unit of capacitance is farads (F).

Dielectric Material

• A dielectric material is an insulating material that is placed between the plates of a capacitor to increase the capacitance.
• It reduces the effective electric field between the plates and stores more charge for the same potential difference.
• Common dielectric materials include air, paper, mica, and various types of plastics.

Dielectric Constant

• The dielectric constant, also known as the relative permittivity, is a measure of how effectively a dielectric material stores electrical energy.
• It is represented by the symbol κ and is defined as the ratio of the electric field in a vacuum to the electric field in the dielectric material.
• The dielectric constant of a vacuum is 1.

Calculating Capacitance with Dielectric Material

• When a dielectric material is inserted between the plates of a capacitor, the capacitance increases by a factor of the dielectric constant.
• Mathematically, the new capacitance C’ = κ * C, where C is the original capacitance and κ is the dielectric constant.

Applications of Capacitors

• Capacitors are widely used in various electrical and electronic devices.
• They are used for energy storage, filtering, timing, voltage regulation, coupling, and decoupling in circuits.
• Capacitors are also used in power factor correction, motor starters, electronic oscillators, and radio frequency applications.

Summary

• Electric field and electric potential are important concepts in physics.
• Capacitance is the ability of a system to store electrical energy.
• Capacitors can be connected in series or parallel to modify the total capacitance.
• The energy stored in a capacitor can be calculated using the formula E = 0.5 * C * V².
• Dielectric materials increase the capacitance of a capacitor.
• Capacitors have various applications in electrical and electronic devices.