Electric Field And Potential And Concept Of Capacitance

• Introduction to Electric Field
• Definition of Electric Field
• Electric Field of a Point Charge
• Electric Field of Multiple Point Charges
• Electric Field due to Continuous Charge Distribution

Electric Field And Potential And Concept Of Capacitance

• Introduction to Electric Potential
• Definition of Electric Potential
• Electric Potential Difference
• Relation between Electric Field and Electric Potential
• Electric Potential due to Point Charges

Electric Field And Potential And Concept Of Capacitance

• Equipotential Surfaces
• Electric Potential due to Continuous Charge Distribution
• Capacitors and Capacitance
• Capacitance of a Parallel Plate Capacitor
• Calculation of Capacitance of Parallel Plate Capacitor

Electric Field And Potential And Concept Of Capacitance

• Combination of Capacitors
• Capacitors in Series
• Capacitors in Parallel
• Energy Stored in a Capacitor
• Calculation of Energy Stored in a Capacitor

Electric Field And Potential And Concept Of Capacitance

• Dielectrics and Insulators
• Definition of Dielectric Constant
• Effect of Dielectric on Capacitance
• Capacitance with Different Dielectrics
• Definition of Electric Flux

Note: Please continue from Slide 11.

Electric Field And Potential And Concept Of Capacitance - Clarify with the Conductor

• Electric Field inside a Conductor
• Electric Field on the surface of a Conductor
• Electric Potential inside a Conductor
• Equipotential Surfaces inside a Conductor
• Electric Field and Potential near a Conductor Edge

Electric Field And Potential And Concept Of Capacitance - Gauss’s Law

• Gauss’s Law
• Statement of Gauss’s Law
• Flux through a Closed Surface
• Electric Flux of a Point Charge
• Electric Flux of a Uniformly Charged Sphere

Electric Field And Potential And Concept Of Capacitance - Gauss’s Law (Contd.)

• Gauss’s Law for a Conductor
• Electric Field at the Surface of a Conductor
• Electric Field inside a Hollow Conductor
• Electric Field inside a Solid Conductor
• Applications of Gauss’s Law

Electric Field And Potential And Concept Of Capacitance - Potential due to a Distributed Charge

• Potential due to a Uniformly Charged Sphere
• Potential due to a Uniformly Charged Ring
• Potential due to a Line of Charge
• Potential due to a Plane Sheet of Charge
• Potential due to a Disc of Charge

Electric Field And Potential And Concept Of Capacitance - Potential due to Multiple Point Charges

• Potential due to Multiple Point Charges
• Potential due to Two Point Charges
• Potential of a Dipole
• Electric Potential due to a System of Point Charges
• Calculation of Electric Potential

Electric Field And Potential And Concept Of Capacitance - Capacitance of Spherical and Cylindrical Capacitors

• Capacitance of a Sphere
• Capacitance of a Parallel Plate Capacitor (Dielectric)
• Spherical Capacitor and its Capacitance
• Cylindrical Capacitor and its Capacitance
• Combination of Capacitors (Series and Parallel)

Electric Field And Potential And Concept Of Capacitance - Energy Stored in Capacitors

• Energy Stored in a Capacitor
• Capacitors in Series (Energy Stored)
• Capacitors in Parallel (Energy Stored)
• Dielectrics and Energy Stored
• Calculation of Energy Stored in a Capacitor

Electric Field And Potential And Concept Of Capacitance - Electric Potential and Work Done

• Work Done by an External Force
• Work Done to Move a Charge
• Potential Difference as Work Done per unit Charge
• Electrostatic Potential Energy
• Relationship between Potential Difference and Work Done

Electric Field And Potential And Concept Of Capacitance - Electric Field Due to an Electric Dipole

• Electric Field due to an Electric Dipole at Different Points
• Electric Field on the Axis of an Electric Dipole
• Electric Field on the Equatorial Plane of an Electric Dipole
• Electric Potential due to an Electric Dipole
• Potential Energy of an Electric Dipole in an Electric Field

Electric Field And Potential And Concept Of Capacitance - Clarity with the Conductor

• Electric Field inside a Conductor:
  • The electric field inside a conductor is zero in electrostatic equilibrium.
  • This is due to the fact that charges within the conductor redistribute themselves to cancel out any external electric field.
• Electric Field on the surface of a Conductor:
  • The electric field just outside the surface of a charged conductor is perpendicular to the surface.
  • The electric field is strongest where the surface is most curved (e.g., sharp points).
• Electric Potential inside a Conductor:
  • The electric potential is constant throughout the bulk of a conductor in electrostatic equilibrium.
  • The electric potential just inside the surface of a conductor is equal to the potential on the surface.
• Equipotential Surfaces inside a Conductor:
  • Inside a conductor, all points on the same equipotential surface have the same potential.
  • Equipotential surfaces are perpendicular to the electric field lines.
• Electric Field and Potential near a Conductor Edge:
  • Near the edge of a conductor, the electric field is stronger and directed perpendicular to the surface.
  • The potential decreases as we move away from the conductor’s surface.

Electric Field And Potential And Concept Of Capacitance - Gauss’s Law

• Gauss’s Law:
  • Gauss’s Law relates the total electric flux through a closed surface to the total charge enclosed by the surface.
  • It provides an alternative method to calculate electric fields using symmetry.
• Statement of Gauss’s Law:
  • The total electric flux through any closed surface is equal to the net charge enclosed divided by the permittivity of free space.
• Flux through a Closed Surface:
  • Electric flux is defined as the dot product of the electric field and a differential area vector.
  • It represents the total number of electric field lines passing through a given area.
• Electric Flux of a Point Charge:
  • The electric flux through a closed surface surrounding a point charge is given by Φ = q/ε₀, where q is the charge and ε₀ is the permittivity of free space.
• Electric Flux of a Uniformly Charged Sphere:
  • The electric flux through a closed surface surrounding a uniformly charged sphere is Φ = q_enclosed/ε₀, where q_enclosed is the charge enclosed.

Electric Field And Potential And Concept Of Capacitance - Gauss’s Law (Contd.)

• Gauss’s Law for a Conductor:
  • The electric field just outside the surface of a charged conductor is perpendicular to the surface and its magnitude is σ/ε₀, where σ is the surface charge density.
• Electric Field at the Surface of a Conductor:
  • The electric field just outside the surface of a charged conductor is normal to the surface and its magnitude is given by E = σ/ε₀, with direction away from positively charged surface.
• Electric Field inside a Hollow Conductor:
  • In the presence of a hollow conductor, the electric field inside the hollow part is zero in electrostatic equilibrium.
  • Charges redistribute on the outer surface of the conductor to cancel out any external electric field.
• Electric Field inside a Solid Conductor:
  • In a solid conductor, the electric field inside is zero in electrostatic equilibrium.
  • Charges redistribute throughout the conductor to cancel out any external electric field.
• Applications of Gauss’s Law:
  • Gauss’s Law can be used to find electric fields and potentials for symmetrical charge distributions.
  • It provides a simplified approach to solving electrostatic problems.

Electric Field And Potential And Concept Of Capacitance - Potential due to a Distributed Charge

• Potential due to a Uniformly Charged Sphere:
  • The electric potential due to a uniformly charged solid sphere at a point outside the sphere is given by V = k(q/r), where q is the charge, r is the distance from the center, and k is the electrostatic constant.
• Potential due to a Uniformly Charged Ring:
  • The electric potential due to a uniformly charged ring at a point on its axis is given by V = k(q/R) * (√(x^2 + R^2) - |x|), where q is the charge, R is the radius of the ring, and x is the distance from the center of the ring.
• Potential due to a Line of Charge:
  • The electric potential due to a line of charge at a point perpendicular to the line is given by V = k(λ/r), where λ is the linear charge density and r is the distance from the line.
• Potential due to a Plane Sheet of Charge:
  • The electric potential due to a uniformly charged plane sheet at a point perpendicular to the sheet is given by V = 2πkσ, where σ is the surface charge density.
• Potential due to a Disc of Charge:
  • The electric potential due to a uniformly charged disc at a point on its axis is given by V = (kσR²)/(2√(x^2 + R^2)), where σ is the surface charge density, R is the radius of the disc, and x is the distance from the center.

Electric Field And Potential And Concept Of Capacitance - Potential due to Multiple Point Charges

• Potential due to Multiple Point Charges:
  • The electric potential at a point due to multiple point charges is the algebraic sum of the potentials due to each individual charge.
• Potential due to Two Point Charges:
  • The electric potential at a point due to two point charges is given by V = k(q1/r1 + q2/r2), where q1 and q2 are the charges, r1 and r2 are the distances from the charges, and k is the electrostatic constant.
• Potential of a Dipole:
  • The electric potential at a point on the axis of a dipole is given by V = (kpd)/(r² - d²)^(1/2), where p is the dipole moment, d is the separation between the charges, and r is the distance from the center of the dipole.
• Electric Potential due to a System of Point Charges:
  • The electric potential at a point due to a system of point charges is the algebraic sum of the potentials due to each individual charge.
• Calculation of Electric Potential:
  • The electric potential at a point can be calculated using the formula V = kQ/r, where Q is the total charge and r is the distance from the point charge.

Electric Field And Potential And Concept Of Capacitance - Capacitance of Spherical and Cylindrical Capacitors

• Capacitance of a Sphere:
  • The capacitance of a conducting sphere is given by C = 4πε₀R, where R is the radius of the sphere and ε₀ is the permittivity of free space.
• Capacitance of a Parallel Plate Capacitor (Dielectric):
  • The capacitance of a parallel plate capacitor with a dielectric material between the plates is given by C’ = κC, where κ is the dielectric constant and C is the capacitance without the dielectric.
• Spherical Capacitor and its Capacitance:
  • A spherical capacitor consists of two concentric conducting spheres.
  • The capacitance of a spherical capacitor is given by C = 4πε₀(1/r₁ - 1/r₂), where r₁ and r₂ are the radii of the inner and outer spheres.
• Cylindrical Capacitor and its Capacitance:
  • A cylindrical capacitor consists of two long coaxial cylinders.
  • The capacitance of a cylindrical capacitor is given by C = 2πε₀L/(ln(b/a)), where L is the length of the cylinders, a is the radius of the inner cylinder, and b is the radius of the outer cylinder.
• Combination of Capacitors (Series and Parallel):
  • Capacitors can be connected in series or parallel to obtain different equivalent capacitances.
  • In series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
  • In parallel, the equivalent capacitance is equal to the sum of the individual capacitances.

Electric Field And Potential And Concept Of Capacitance - Energy Stored in Capacitors

• Energy Stored in a Capacitor:
  • The energy stored in a capacitor can be calculated using the equation U = (1/2)CV², where U is the energy, C is the capacitance, and V is the potential difference across the capacitor.
• Capacitors in Series (Energy Stored):
  • The total energy stored in capacitors connected in series is the sum of the energies stored in each individual capacitor.
• Capacitors in Parallel (Energy Stored):
  • The total energy stored in capacitors connected in parallel is equal to the sum of the energies stored in each individual capacitor.
• Dielectrics and Energy Stored:
  • When a dielectric material is inserted between the plates of a capacitor, the energy stored in the capacitor increases by a factor of κ, the dielectric constant.
• Calculation of Energy Stored in a Capacitor:
  • The energy stored in a capacitor can also be calculated using the equation U = (1/2)QV, where Q is the charge stored and V is the potential difference across the capacitor.

Electric Field And Potential And Concept Of Capacitance - Electric Potential and Work Done

• Work Done by an External Force:
  • Work is done when a force moves an object through a displacement in the direction of the force.
• Work Done to Move a Charge:
  • When an external force moves a positive charge in an electric field, work is done on the charge.
  • The work done is given by W = q(Vf - Vi), where q is the charge, Vf is the final potential, and Vi is the initial potential.
• Potential Difference as Work Done per unit Charge:
  • The potential difference between two points is defined as the work done per unit charge in moving a positive test charge from one point to the other.
  • Mathematically, ΔV = W/q, where ΔV is the potential difference, W is the work done, and q is the charge.
• Electrostatic Potential Energy:
  • The potential energy of a system of charges in an electric field is the work done in assembling the system of charges.
  • The electric potential energy of charges q₁ and q₂ separated by a distance r is given by PE = k(q₁q₂)/r, where k is the electrostatic constant.
• Relationship between Potential Difference and Work Done:
  • The work done in moving a charge q through a potential difference ΔV is given by W = qΔV.
  • It is equal to the change in potential energy of the charge.

Electric Field And Potential And Concept Of Capacitance - Electric Field Due to an Electric Dipole

• Electric Field due to an Electric Dipole at Different Points:
  • At a point along the axial line of an electric dipole, the electric field is directed away from the positive charge and towards the negative charge.
  • At a point on the equatorial plane of an electric dipole, the electric field points in the perpendicular direction.
• Electric Field on the Axis of an Electric Dipole:
  • The electric field at a point on the axial line of an electric dipole is given by E = (kp)/(r² + (d/2)²)^(3/2), where p is the dipole moment, r is the distance from the center of the dipole, and d is the separation between the charges.
• Electric Field on the Equatorial Plane of an Electric Dipole:
  • The electric field at a point on the equatorial plane of an electric dipole is given by E = (kp)/(r² + (d/2)²)^(3/2), where p is the dipole moment, r is the distance from the center of the dipole, and d is the separation between the charges.
• Electric Potential due to an Electric Dipole:
  • The electric potential at a point due to an electric dipole is given by V = (kp cosθ)/(r²), where p is the dipole moment, θ is the angle between the dipole axis and the line joining the dipole to the point, and r is the distance from the center of the dipole.
• Potential Energy of an Electric Dipole in an Electric Field:
  • The potential energy of an electric dipole in an electric field is given by PE = -pE, where p is the dipole moment and E is the electric field.