Electric Field and Potential

Electric Field:

• Electric field due to a point charge:

  • Inverse square law: The electric field due to a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge.
  • Electric field lines: Electric field lines are imaginary lines that represent the direction and strength of the electric field.

  Reference: NCERT Class 12, Chapter 1: Electric Charges and Fields

• Electric field due to a dipole:

  • A dipole is a pair of equal and opposite charges separated by a small distance. The electric field due to a dipole is proportional to the magnitude of the charges, the distance between the charges, and the orientation of the dipole.

  Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Electric field due to a continuous charge distribution:

• The electric field due to a continuous charge distribution like that of a charged sphere is obtained by integrating the contributions due to individual point charges within the distribution.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Electric field lines:
  • Electric field lines are imaginary lines that show the path a positive test charge would take if placed in the field.
  • Electric field lines start from positive charges and end at negative charges.
  • The density of electric field lines indicates the strength of the electric field.

  Reference: NCERT Class 12, Chapter 1: Electric Charges and Fields

Electric Potential:

• Electric potential due to a point charge:

  • Electric potential at a point due to a point charge is defined as the amount of electric potential energy per unit positive charge.
  • It is directly proportional to the magnitude of the charge and inversely proportional to the distance from the charge.

  Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Electric potential due to a dipole:

• The electric potential due to a dipole depends on the magnitude of the charges, the distance between the charges, and the orientation of the dipole with respect to the point of observation.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Electric potential due to a continuous charge distribution:
• The electric potential due to a continuous charge distribution is obtained by integrating the contributions due to individual point charges within the distribution.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Electric potential surfaces:
• Electric potential surfaces are surfaces in space at which the electric potential is constant.
• Electric field lines are perpendicular to electric potential surfaces.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Potential difference:
• Potential difference between two points is the difference in electric potential between those points.
• It is the amount of work done in moving a positive charge from one point to another.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Work done by an electric field:
• The work done by an electric field in moving a positive charge from one point to another is equal to the negative change in electric potential between those points.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

Conductors and Insulators:

• Properties of conductors and insulators:
  • Conductors allow electric charge to flow easily, while insulators do not.
  • Conductors have free electrons that can move easily, while insulators lack these.

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Ohmic conductors and superconductors:
  • Ohmic conductors obey Ohm’s law, which states that the current through a conductor is directly proportional to the voltage across it.
  • Superconductors are materials that conduct electricity with zero resistance below a certain critical temperature.

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Capacitors and dielectrics:
• A capacitor is a device that stores electrical energy in an electric field.
• A capacitor consists of two conducting plates separated by an insulating material called a dielectric.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Polarization of dielectrics:
• Polarization is the phenomenon of aligning the dipoles of a dielectric material in the presence of an external electric field.
• Dielectric polarization increases the capacitance of a capacitor.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

Capacitance

Capacitance:

• Capacitance of a parallel-plate capacitor:
  • Capacitance of a parallel-plate capacitor is directly proportional to the area of the plates, inversely proportional to the distance between the plates, and depends on the permittivity of the material between the plates.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Capacitance of a cylindrical capacitor:
• The capacitance of a cylindrical capacitor is directly proportional to the length of the capacitor, inversely proportional to the distance between the cylinders, and depends on the permittivity of the material between the cylinders.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Capacitance of a spherical capacitor:
• Capacitance of a spherical capacitor is directly proportional to the radius of the outer sphere and inversely proportional to the distance between the spheres.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Combination of capacitors:
• Capacitors can be connected in series or in parallel. -Capacitors in series have the same charge, while capacitors in parallel have the same potential difference.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

• Energy stored in a capacitor:
  • The energy stored in a capacitor is directly proportional to capacitance, the square of the voltage across the capacitor, and inversely proportional to two.

Reference: NCERT Class 12, Chapter 2: Electrostatic Potential and Capacitance

Applications of Capacitors:

• Capacitors in DC circuits:
  • Capacitors in DC circuits block the flow of direct current while allowing alternating current to pass.
  • Capacitors are used for smoothing the output of rectifiers.

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Capacitors in AC circuits:
• Capacitors in AC circuits store and release electrical energy, causing a phase difference between current and voltage.
• Capacitors are used in AC filters and tuning circuits.

Reference: NCERT Class 12, Chapter 7: Alternating Current

• Filters and oscillators:
• Capacitors are used along with resistors and/or inductors to form filters that remove unwanted frequency components from electrical signals.
• Capacitors are used in oscillators to generate alternating currents of specific frequencies.

Reference: NCERT Class 12, Chapter 7: Alternating Current

• Capacitors in electronic devices:
• Capacitors are extensively used in electronic devices for various purposes such as filtering, smoothing, timing, and energy storage.
• They play a crucial role in electronic circuits like power supplies, amplifiers, and digital systems.

Reference: NCERT Class 12, Chapter 14: Semiconductor Electronics: Materials, Devices and Simple Circuits