Slide 1
- Topic: Potential Due to Different Charge Distributions - Potential due to an infinite linear charge density
- Introduction to potential energy and potential difference
- Definition of electric potential
- Review of Coulomb’s Law and electric field
- Relationship between electric field and potential
Slide 2
- Derivation of potential due to an infinite linear charge density
- Calculation of potential at a point along the axis of a uniformly charged rod
- Significance of the linear charge density and distance from the rod
- Example: Finding the potential at a specific distance from a uniformly charged rod
Slide 3
- Potential due to finite linear charge densities
- Calculation of potential at a point along the axis of a uniformly charged rod with nonuniform charge distribution
- Example: Finding the potential at a specific distance from a rod with varying linear charge density
Slide 4
- Potential due to a uniformly charged ring
- Calculation of potential at a point along the axis of a uniformly charged ring
- Significance of the charge on the ring and distance from the ring
- Example: Finding the potential at a specific distance from a uniformly charged ring
Slide 5
- Potential due to a uniformly charged disk
- Calculation of potential at a point along the axis of a uniformly charged disk
- Significance of the charge on the disk and distance from the disk
- Example: Finding the potential at a specific distance from a uniformly charged disk
Slide 6
- Potential due to a uniformly charged sphere
- Calculation of potential at a point outside a uniformly charged sphere
- Significance of the charge on the sphere and distance from the sphere
- Example: Finding the potential at a specific distance from a uniformly charged sphere
Slide 7
- Potential due to a uniformly charged shell
- Calculation of potential at a point inside or outside a uniformly charged shell
- Significance of the charge on the shell and distance from the shell
- Example: Finding the potential at a specific distance from a uniformly charged shell
Slide 8
- Potential due to multiple point charges
- Superposition principle for potential
- Calculation of potential due to multiple point charges at a point
- Example: Finding the net potential at a specific point due to multiple point charges
Slide 9
- Potential due to continuous charge distributions
- Integration method for calculating potential
- Calculation of potential due to continuous charge distribution using integration
- Example: Finding the potential due to a continuous charge distribution
Slide 10
- Summary of potential due to different charge distributions
- Important equations and principles related to potential
- Recap of calculation methods for different charge distributions
- Importance of understanding and applying potential in physics problems
Slide 11
- Equation: V = k * λ / r
- Explanation of Variables:
- V: Electric potential due to the linear charge density
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density (C/m)
- r: Distance from the charged rod (m)
- Example: A rod with a linear charge density of 2 C/m, find the electric potential at a distance of 5 m from the rod.
Slide 12
- Equation: V = k * Σλ / r
- Explanation of Variables:
- V: Electric potential due to the finite linear charge densities
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Σλ: Sum of the linear charge densities (C/m)
- r: Distance from the charged rod (m)
- Example: Two rods with linear charge densities of 3 C/m and -4 C/m, find the electric potential at a distance of 6 m from the rods.
Slide 13
- Equation: V = k * λ * z / (2πε₀ * (z² + R²)^(3/2))
- Explanation of Variables:
- V: Electric potential due to a uniformly charged ring
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density of the ring (C/m)
- z: Distance along the axis of the ring (m)
- R: Radius of the ring (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A ring with a linear charge density of 5 C/m and a radius of 2 m, calculate the electric potential at a distance of 3 m from the ring.
Slide 14
- Equation: V = k * σ / (2ε₀) * (1 - √(1 + R² / (z² + R²)))
- Explanation of Variables:
- V: Electric potential due to a uniformly charged disk
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- σ: Surface charge density of the disk (C/m²)
- z: Distance along the axis of the disk (m)
- R: Radius of the disk (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A disk with a surface charge density of 4 C/m² and a radius of 3 m, find the electric potential at a distance of 2.5 m from the disk.
Slide 15
- Equation: V = k * Q / (4πε₀ * r)
- Explanation of Variables:
- V: Electric potential due to a uniformly charged sphere
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Q: Total charge of the sphere (C)
- r: Distance from the center of the sphere (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A sphere with a charge of 10 C, calculate the electric potential at a distance of 5 m from the center of the sphere.
Slide 16
- Equation (Outside the shell): V = k * Q / (4πε₀ * r)
- Equation (Inside the shell): V = k * Q / (4πε₀ * R)
- Explanation of Variables:
- V: Electric potential due to a uniformly charged shell
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Q: Total charge on the shell (C)
- r: Distance from the center of the shell (m)
- R: Radius of the shell (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A shell with a charge of 8 C and a radius of 4 m, find the electric potential at a distance of 6 m from the center of the shell.
Slide 17
- Equations: V = k * Q1 / r1 + k * Q2 / r2 + k * Q3 / r3 + …
- Explanation:
- Applying the principle of superposition for potential due to multiple point charges
- Adding up the potentials due to each individual point charge
- Example: Three point charges, +2 μC, -3 μC, and +4 μC, are placed at distances of 1 m, 2 m, and 3 m, respectively. Find the net electric potential at a point located 5 m away from the charges.
Slide 18
- Equation: V = k * λ * dr / r
- Explanation of Variables:
- V: Electric potential due to continuous charge distribution
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density (C/m)
- dr: Infinitesimally small length element on the charge distribution (m)
- r: Distance from the charge distribution (m)
- Example: A charge distribution with a linear charge density of 3 C/m, calculate the electric potential at a distance of 4 m from the distribution.
Slide 19
- Summary of different potential equations for various charge distributions
- Importance of understanding potential in analyzing electrostatic systems
- Potential as a scalar quantity and its relationship with electric field
- Applications of calculating potential in engineering and physics fields
Slide 20
- Questions and answers session
- Further resources for studying potential due to different charge distributions
- Encouragement for students to practice solving numerical problems related to potential
- Conclusion of the lecture on potential due to different charge distributions
Slide 21
- Equation: V = k * λ / r
- Explanation of Variables:
- V: Electric potential due to the linear charge density
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density (C/m)
- r: Distance from the charged rod (m)
- Example: A rod with a linear charge density of 2 C/m, find the electric potential at a distance of 5 m from the rod.
Slide 22
- Equation: V = k * Σλ / r
- Explanation of Variables:
- V: Electric potential due to the finite linear charge densities
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Σλ: Sum of the linear charge densities (C/m)
- r: Distance from the charged rod (m)
- Example: Two rods with linear charge densities of 3 C/m and -4 C/m, find the electric potential at a distance of 6 m from the rods.
Slide 23
- Equation: V = k * λ * z / (2πε₀ * (z² + R²)^(3/2))
- Explanation of Variables:
- V: Electric potential due to a uniformly charged ring
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density of the ring (C/m)
- z: Distance along the axis of the ring (m)
- R: Radius of the ring (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A ring with a linear charge density of 5 C/m and a radius of 2 m, calculate the electric potential at a distance of 3 m from the ring.
Slide 24
- Equation: V = k * σ / (2ε₀) * (1 - √(1 + R² / (z² + R²)))
- Explanation of Variables:
- V: Electric potential due to a uniformly charged disk
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- σ: Surface charge density of the disk (C/m²)
- z: Distance along the axis of the disk (m)
- R: Radius of the disk (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A disk with a surface charge density of 4 C/m² and a radius of 3 m, find the electric potential at a distance of 2.5 m from the disk.
Slide 25
- Equation: V = k * Q / (4πε₀ * r)
- Explanation of Variables:
- V: Electric potential due to a uniformly charged sphere
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Q: Total charge of the sphere (C)
- r: Distance from the center of the sphere (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A sphere with a charge of 10 C, calculate the electric potential at a distance of 5 m from the center of the sphere.
Slide 26
- Equation (Outside the shell): V = k * Q / (4πε₀ * r)
- Equation (Inside the shell): V = k * Q / (4πε₀ * R)
- Explanation of Variables:
- V: Electric potential due to a uniformly charged shell
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- Q: Total charge on the shell (C)
- r: Distance from the center of the shell (m)
- R: Radius of the shell (m)
- ε₀: Permittivity of free space (8.85 x 10^-12 C^2 / N m^2)
- Example: A shell with a charge of 8 C and a radius of 4 m, find the electric potential at a distance of 6 m from the center of the shell.
Slide 27
- Equations: V = k * Q1 / r1 + k * Q2 / r2 + k * Q3 / r3 + …
- Explanation:
- Applying the principle of superposition for potential due to multiple point charges
- Adding up the potentials due to each individual point charge
- Example: Three point charges, +2 μC, -3 μC, and +4 μC, are placed at distances of 1 m, 2 m, and 3 m, respectively. Find the net electric potential at a point located 5 m away from the charges.
Slide 28
- Equation: V = k * λ * dr / r
- Explanation of Variables:
- V: Electric potential due to continuous charge distribution
- k: Coulomb’s constant (9 x 10^9 N m^2 / C^2)
- λ: Linear charge density (C/m)
- dr: Infinitesimally small length element on the charge distribution (m)
- r: Distance from the charge distribution (m)
- Example: A charge distribution with a linear charge density of 3 C/m, calculate the electric potential at a distance of 4 m from the distribution.
Slide 29
- Summary of different potential equations for various charge distributions
- Importance of understanding potential in analyzing electrostatic systems
- Potential as a scalar quantity and its relationship with electric field
- Applications of calculating potential in engineering and physics fields
Slide 30
- Questions and answers session
- Further resources for studying potential due to different charge distributions
- Encouragement for students to practice solving numerical problems related to potential
- Conclusion of the lecture on potential due to different charge distributions