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
- 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
- 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
- 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
- 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
- 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
- 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