Potential Due To Different Charge Distributions - Revision

Electrostatic Potential Energy

  • Recap of electrostatic potential energy
  • Definition of potential due to a point charge
  • Equation: V = kQ/r
  • Significance of the equation in understanding electrostatic potential energy
  • Calculation example: Find the electric potential at a distance of 2 m from a point charge of +4 C

Potential Due To Different Charge Distributions

  • Introduction to potential due to different charge distributions
  • Equation: V = ∑(k|q|/r)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), q (charge), and r (distance)
  • Calculation example: Find the electric potential at a point due to three point charges

Potential Due To Uniformly Charged Ring

  • Introduction to potential due to a uniformly charged ring
  • Equation: V = 2kQ / R√R^2 + r^2
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the ring), and r (distance from the center of the ring)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged ring

Potential Due To Uniformly Charged Disc

  • Introduction to potential due to a uniformly charged disc
  • Equation: V = (2kσ / ε₀)√(R^2 + z^2) - √(R^2 + h^2)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), σ (surface charge density), ε₀ (permittivity of free space), R (radius of the disc), z (distance from the center of the disc to the point), and h (height from the plane of the disc to the point)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged disc

Potential Due To Charged Sphere

  • Introduction to potential due to a charged sphere
  • Equation: V = (kQ / R) [3 - (r^2 / R^2)]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the sphere), and r (distance from the center of the sphere to the point)
  • Calculation example: Find the electric potential at a point inside a uniformly charged sphere

Potential Due To Electric Dipole

  • Introduction to potential due to an electric dipole
  • Equation: V = (kp / r^2) [cosθ₁ - cosθ₂]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), p (electric dipole moment), r (distance from the center of the dipole to the point), θ₁ (angle between the dipole axis and the line joining the center of the dipole to the point), and θ₂ (angle between the dipole axis and the line pointing away from the dipole towards the point)
  • Calculation example: Find the electric potential at a point on the axial line of an electric dipole

Equipotential Surfaces

  • Introduction to equipotential surfaces
  • Definition of an equipotential surface
  • Properties of equipotential surfaces
  • Diagrams showing equipotential surfaces for different charge configurations
  • Example: Equipotential surface around a point charge

Relationship Between Electric Field and Electric Potential

  • Explanation of the relationship between electric field and electric potential
  • Definition of electric field and electric potential
  • Mathematical relationship: E = -∇V
  • Interpretation of the equation in terms of electric field lines and equipotential surfaces
  • Diagram illustrating the relationship between electric field lines and equipotential surfaces

Calculating Electric Field from Electric Potential

  • Introduction to calculating electric field from electric potential
  • Equation: E = -∇V
  • Explanation of each term in the equation: E (electric field), ∇ (del or nabla operator), and V (electric potential)
  • Calculation example: Find the electric field at a point due to a point charge

Calculating Electric Potential from Electric Field

  • Introduction to calculating electric potential from electric field
  • Equation: V = -∫E • dl
  • Explanation of each term in the equation: V (electric potential), E (electric field), and dl (infinitesimal displacement vector)
  • Calculation example: Find the electric potential at a point due to a uniform electric field

Potential Due To Different Charge Distributions - Revision

Electrostatic Potential Energy

  • Recap of electrostatic potential energy
  • Definition of potential due to a point charge
  • Equation: V = kQ/r
  • Significance of the equation in understanding electrostatic potential energy
  • Calculation example: Find the electric potential at a distance of 2 m from a point charge of +4 C

Potential Due To Different Charge Distributions

  • Introduction to potential due to different charge distributions
  • Equation: V = ∑(k|q|/r)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), q (charge), and r (distance)
  • Calculation example: Find the electric potential at a point due to three point charges

Potential Due To Uniformly Charged Ring

  • Introduction to potential due to a uniformly charged ring
  • Equation: V = 2kQ / R√R^2 + r^2
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the ring), and r (distance from the center of the ring)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged ring

Potential Due To Uniformly Charged Disc

  • Introduction to potential due to a uniformly charged disc
  • Equation: V = (2kσ / ε₀)√(R^2 + z^2) - √(R^2 + h^2)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), σ (surface charge density), ε₀ (permittivity of free space), R (radius of the disc), z (distance from the center of the disc to the point), and h (height from the plane of the disc to the point)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged disc

Potential Due To Charged Sphere

  • Introduction to potential due to a charged sphere
  • Equation: V = (kQ / R) [3 - (r^2 / R^2)]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the sphere), and r (distance from the center of the sphere to the point)
  • Calculation example: Find the electric potential at a point inside a uniformly charged sphere

Potential Due To Electric Dipole

  • Introduction to potential due to an electric dipole
  • Equation: V = (kp / r^2) [cosθ₁ - cosθ₂]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), p (electric dipole moment), r (distance from the center of the dipole to the point), θ₁ (angle between the dipole axis and the line joining the center of the dipole to the point), and θ₂ (angle between the dipole axis and the line pointing away from the dipole towards the point)
  • Calculation example: Find the electric potential at a point on the axial line of an electric dipole

Equipotential Surfaces

  • Introduction to equipotential surfaces
  • Definition of an equipotential surface
  • Properties of equipotential surfaces
  • Diagrams showing equipotential surfaces for different charge configurations
  • Example: Equipotential surface around a point charge

Relationship Between Electric Field and Electric Potential

  • Explanation of the relationship between electric field and electric potential
  • Definition of electric field and electric potential
  • Mathematical relationship: E = -∇V
  • Interpretation of the equation in terms of electric field lines and equipotential surfaces
  • Diagram illustrating the relationship between electric field lines and equipotential surfaces

Calculating Electric Field from Electric Potential

  • Introduction to calculating electric field from electric potential
  • Equation: E = -∇V
  • Explanation of each term in the equation: E (electric field), ∇ (del or nabla operator), and V (electric potential)
  • Calculation example: Find the electric field at a point due to a point charge

Calculating Electric Potential from Electric Field

  • Introduction to calculating electric potential from electric field
  • Equation: V = -∫E • dl
  • Explanation of each term in the equation: V (electric potential), E (electric field), and dl (infinitesimal displacement vector)
  • Calculation example: Find the electric potential at a point due to a uniform electric field

Potential Due To Different Charge Distributions - Revision

Electrostatic Potential Energy

  • Recap of electrostatic potential energy
  • Definition of potential due to a point charge
  • Equation: V = kQ/r
  • Significance of the equation in understanding electrostatic potential energy
  • Calculation example: Find the electric potential at a distance of 2 m from a point charge of +4 C

Potential Due To Different Charge Distributions

  • Introduction to potential due to different charge distributions
  • Equation: V = ∑(k|q|/r)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), q (charge), and r (distance)
  • Calculation example: Find the electric potential at a point due to three point charges

Potential Due To Uniformly Charged Ring

  • Introduction to potential due to a uniformly charged ring
  • Equation: V = 2kQ / R√R^2 + r^2
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the ring), and r (distance from the center of the ring)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged ring

Potential Due To Uniformly Charged Disc

  • Introduction to potential due to a uniformly charged disc
  • Equation: V = (2kσ / ε₀)√(R^2 + z^2) - √(R^2 + h^2)
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), σ (surface charge density), ε₀ (permittivity of free space), R (radius of the disc), z (distance from the center of the disc to the point), and h (height from the plane of the disc to the point)
  • Calculation example: Find the electric potential at a point on the axis of a uniformly charged disc

Potential Due To Charged Sphere

  • Introduction to potential due to a charged sphere
  • Equation: V = (kQ / R) [3 - (r^2 / R^2)]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), Q (charge), R (radius of the sphere), and r (distance from the center of the sphere to the point)
  • Calculation example: Find the electric potential at a point inside a uniformly charged sphere

Potential Due To Electric Dipole

  • Introduction to potential due to an electric dipole
  • Equation: V = (kp / r^2) [cosθ₁ - cosθ₂]
  • Explanation of each term in the equation: V (electric potential), k (Coulomb’s constant), p (electric dipole moment), r (distance from the center of the dipole to the point), θ₁ (angle between the dipole axis and the line joining the center of the dipole to the point), and θ₂ (angle between the dipole axis and the line pointing away from the dipole towards the point)
  • Calculation example: Find the electric potential at a point on the axial line of an electric dipole

Equipotential Surfaces

  • Introduction to equipotential surfaces
  • Definition of an equipotential surface
  • Properties of equipotential surfaces
  • Diagrams showing equipotential surfaces for different charge configurations
  • Example: Equipotential surface around a point charge

Relationship Between Electric Field and Electric Potential

  • Explanation of the relationship between electric field and electric potential
  • Definition of electric field and electric potential
  • Mathematical relationship: E = -∇V
  • Interpretation of the equation in terms of electric field lines and equipotential surfaces
  • Diagram illustrating the relationship between electric field lines and equipotential surfaces

Calculating Electric Field from Electric Potential

  • Introduction to calculating electric field from electric potential
  • Equation: E = -∇V
  • Explanation of each term in the equation: E (electric field), ∇ (del or nabla operator), and V (electric potential)
  • Calculation example: Find the electric field at a point due to a point charge

Calculating Electric Potential from Electric Field

  • Introduction to calculating electric potential from electric field
  • Equation: V = -∫E • dl
  • Explanation of each term in the equation: V (electric potential), E (electric field), and dl (infinitesimal displacement vector)
  • Calculation example: Find the electric potential at a point due to a uniform electric field