Potential Due To Different Charge Distributions - Superposition Principle In Calculating Potential At A Point

Lecture on Potential Due To Different Charge Distributions - Superposition principle in calculating potential at a point

Slide 1

Introduction to potential due to different charge distributions
Definition of potential at a point
Overview of the superposition principle

Slide 2

Potential due to a point charge
- Formula: V = k * q / r
- Example: Calculating the potential due to a +2 μC charge at a distance of 5 m

Slide 3

Potential due to a system of point charges
- Superposition principle: V_total = V1 + V2 + V3 + …
- Example: Calculating the total potential due to a system of two point charges

Slide 4

Potential due to a continuous charge distribution
- Formula: V = ∫ k * dq / r
- Example: Calculating the potential due to a uniformly charged rod

Slide 5

Potential due to a uniformly charged ring
- Formula: V = k * Q * (z / (z^2 + R^2)^(3/2)) * dz
- Example: Calculating the potential at a point on the axis of a charged ring

Slide 6

Potential due to a uniformly charged disk
- Formula: V = (k * Q * z) / (2 * sqrt(R^2 + z^2))
- Example: Calculating the potential at a point on the axis of a charged disk

Slide 7

Potential due to a spherically symmetric charge distribution
- Formula: V = k * Q / r
- Example: Calculating the potential due to a uniformly charged sphere

Slide 8

Potential due to a non-spherically symmetric charge distribution
- Superposition principle still applies
- Example: Calculating the potential due to a non-uniformly charged spherical shell

Slide 9

Example: Calculating the total potential due to a combination of point charges and continuous charge distributions

Slide 10

Summary of key points covered
Importance of understanding potential due to different charge distributions
Overview of the next topic to be covered

Slide 11

Summary of key points covered so far
Reminder of the superposition principle in calculating potential at a point
Importance of understanding potential due to different charge distributions
Overview of the next topic to be covered

Slide 12

Potential due to a line of charge
- Formula: V = (k * λ) * ln(R2/R1)
- Example: Calculating the potential due to a uniformly charged line segment
Potential due to a charged sphere at a point outside the sphere
- Formula: V = (k * Q) / r
- Example: Calculating the potential at a point outside a uniformly charged sphere
Potential due to a charged sphere at a point inside the sphere
- Formula: V = (k * Q * r) / R^3
- Example: Calculating the potential at a point inside a uniformly charged sphere
Potential due to a charged sphere at the surface of the sphere
- Formula: V = (k * Q) / R
- Example: Calculating the potential at the surface of a uniformly charged sphere

Slide 13

Potential due to a charged cylinder at a point inside the cylinder
- Formula: V = (k * λ * r^2) / (2ε0)
- Example: Calculating the potential at a point inside a uniformly charged cylinder
Potential due to a charged cylinder at a point outside the cylinder
- Formula: V = (k * λ * L) / (2πε0) * ln((R + sqrt(R^2 + L^2)) / (R - sqrt(R^2 + L^2)))
- Example: Calculating the potential at a point outside a uniformly charged cylinder

Slide 14

Potential due to a charged disk at a point on the axis of the disk
- Formula: V = (k * σ) * (sqrt(R^2 + z^2) - z)
- Example: Calculating the potential at a point on the axis of a uniformly charged disk
Potential due to a charged disk at a point off the axis of the disk
- Formula: V = (k * σ * z) / (2ε0 * (sqrt(R^2 + z^2)))
- Example: Calculating the potential at a point off the axis of a uniformly charged disk

Slide 15

Potential due to a charged cylinder at a point on the axis of the cylinder
- Formula: V = (k * λ * R^2) / (2ε0 * sqrt(R^2 + z^2))
- Example: Calculating the potential at a point on the axis of a uniformly charged cylinder
Potential due to a charged cylinder at a point off the axis of the cylinder
- Formula: V = (k * λ * z * ln((R + sqrt(R^2 + z^2)) / (sqrt(R^2 + z^2))))
- Example: Calculating the potential at a point off the axis of a uniformly charged cylinder

Slide 16

Potential due to a charged disk with a hole at a point on the axis of the disk
- Formula: V = (k * σ * (2R + d)) / (2ε0) * ln((R + sqrt(R^2 + d^2)) / (sqrt(R^2 + d^2)))
- Example: Calculating the potential at a point on the axis of a disk with a central hole

Slide 17

Electrostatic potential energy
- Formula: U = q * V
- Example: Calculating the electrostatic potential energy of a charge in a uniform electric field
Electric potential due to a uniformly charged infinite plane
- Formula: V = (σ * d) / (2ε0)
- Example: Calculating the potential at a point near a uniformly charged infinite plane

Slide 18

Electric potential due to a dipole at a point along its axis
- Formula: V = (k * p * cosθ) / (r^2)
- Example: Calculating the potential at a point along the axis of an electric dipole
Electric potential due to a dipole at a point in the equatorial plane
- Formula: V = (k * p * sinθ) / (r^2)
- Example: Calculating the potential at a point in the equatorial plane of an electric dipole

Slide 19

Electric potential due to a dipole at a point in space
- Formula: V = (k * p) / (r^2) * cosθ / r
- Example: Calculating the potential at a general point in space due to an electric dipole
Relationship between electric field and potential
- Formula: E = -∇V
- Example: Understanding the relationship between electric field and potential

Slide 20

Summary of key points covered
Importance of understanding the potential due to different charge distributions
Overview of the next topic to be covered

Slide 21

Capacitors and capacitance
- Definition of capacitance
- Formula: C = Q / V
- Example: Calculating the capacitance of a parallel plate capacitor
Energy stored in a capacitor
- Formula: U = (1/2) * C * V^2
- Example: Calculating the energy stored in a capacitor
Dielectric material and its effect on capacitance
- Explanation of dielectric material
- Formula: C’ = κ * C
- Example: Calculating the new capacitance with a dielectric material

Slide 22

Combination of capacitors
- Series combination of capacitors
  - Equation: C_eq = (1/C1) + (1/C2) + (1/C3) + …
  - Example: Calculating the equivalent capacitance of capacitors in series
Parallel combination of capacitors
- Equation: C_eq = C1 + C2 + C3 + …
- Example: Calculating the equivalent capacitance of capacitors in parallel
Application of capacitors in electronic circuits
- Brief explanation of capacitors’ use in smoothing and filtering circuits

Slide 23

Electric current and its characteristics
- Definition of electric current
- Equation: I = Q / t
- Example: Calculating the current given the charge and time
Electric potential difference and voltage
- Definition of voltage
- Equation: V = W / Q
- Example: Calculating the voltage given the work done and charge
Ohm’s Law
- Equation: V = I * R
- Example: Calculating the resistance given the voltage and current

Slide 24

Resistors and their types
- Brief explanation of resistors
- Different types of resistors: fixed and variable resistors
Resistivity and conductivity
- Definition of resistivity
- Equation: R = ρ * (L / A)
- Example: Calculating the resistance given the resistivity, length, and cross-sectional area
Temperature dependence of resistance
- Explanation of how resistivity changes with temperature

Slide 25

Combination of resistors
- Series combination of resistors
  - Equation: R_eq = R1 + R2 + R3 + …
  - Example: Calculating the equivalent resistance of resistors in series
Parallel combination of resistors
- Equation: (1/R_eq) = (1/R1) + (1/R2) + (1/R3) + …
- Example: Calculating the equivalent resistance of resistors in parallel
Application of resistors in circuits
- Brief explanation of resistors’ use in voltage dividers and current limiters

Slide 26

Kirchhoff’s laws
- Explanation of Kirchhoff’s laws (junction rule and loop rule)
- Application of Kirchhoff’s laws in solving circuit problems
Series and parallel combination of resistors in circuits
- Explanation of how resistors are combined in series and parallel in practical circuits
- Calculation examples for series and parallel combinations

Slide 27

Introduction to magnetic effects of electric current
- Explanation of magnetic field and magnetic force
Magnetic field due to a straight conductor carrying current
- Equation: B = (μ0 * I) / (2π * r)
- Example: Calculating the magnetic field at a distance from a straight conductor
Magnetic field due to a circular loop carrying current
- Equation: B = (μ0 * I * R^2) / (2 * (R^2 + x^2)^(3/2))
- Example: Calculating the magnetic field at a point on the axis of a circular loop

Slide 28

Magnetic field due to a solenoid
- Equation: B = (μ0 * N * I) / L
- Example: Calculating the magnetic field inside a solenoid
Magnetic force on a current-carrying conductor in a magnetic field
- Equation: F = I * L * B * sinθ
- Example: Calculating the force on a current-carrying conductor in a magnetic field
Magnetic force on a moving charged particle in a magnetic field
- Equation: F = q * v * B * sinθ
- Example: Calculating the force on a moving charged particle in a magnetic field

Slide 29

Magnetic force on a current-carrying loop in a magnetic field
- Equation: F = I * A * B * sinθ
- Example: Calculating the force on a current-carrying loop in a magnetic field
Electric motors
- Explanation of how electric motors work using the interaction between magnetic field and current-carrying loop
Magnetic induction and Faraday’s Law of electromagnetic induction
- Explanation of magnetic induction and Faraday’s Law
- Equation: ε = -N * (dΦ/dt)
- Example: Calculating the induced emf using Faraday’s Law

Slide 30

Lenz’s Law
- Explanation of Lenz’s Law and the direction of induced current
Transformers
- Explanation of how transformers work using electromagnetic induction
- Calculation examples for the turns ratio and voltage/current transformations in transformers
Summary of key points covered throughout the lecture
Importance of understanding the topics covered in preparing for the 12th Boards exam