Coulombs law from Gauss theorem

 Deriving Coulomb's Law from Gauss's Theorem

Gauss's theorem states: Φ = Q / ε₀


For a point charge, consider a spherical Gaussian surface:


1. Electric flux Φ = E × 4πr² (surface area of sphere)

2. From Gauss's theorem, Φ = Q / ε₀

3. Equating both, E × 4πr² = Q / ε₀

4. E = Q / (4πε₀r²)


Force on a test charge q: F = qE = qQ / (4πε₀r²)


This is Coulomb's law: F = k * qQ / r², where k = 1 / (4πε₀)b

Comments

Post a Comment

Popular posts from this blog

Electric Dipole

  Electric Dipole  An electric dipole consists of two equal and opposite charges separated by a small distance. It's a fundamental concept in physics. Key Characteristics:  1. Dipole Moment: p = qd, where q is the charge and d is the separation distance. 2. Electric Field: The electric field due to a dipole decreases rapidly with distance. 3. Torque : A dipole experiences a torque in an external electric field.  Applications:  1. Molecular Interactions: Electric dipoles play a crucial role in understanding molecular interactions and properties. 2. Polar Molecules: Molecules with a permanent electric dipole moment. 3. Dielectric Materials: Electric dipoles are induced in dielectric materials in an external electric field. Some examples related to electric dipoles: 1. Water Molecule: A polar molecule with a permanent electric dipole moment. 2. Electric Field Lines: Dipole electric field lines emerge from the positive charge and enter the negative charge. 3...
Read more

Continuous Charge Distribution

 Continuous Charge Distribution  A continuous charge distribution refers to a system where charge is spread over a region, such as a line, surface, or volume. The electric field due to a continuous charge distribution can be calculated using integration. Types of Continuous Charge Distributions: 1. Linear Charge Distribution: Charge is distributed along a line. 2. Surface Charge Distribution: Charge is distributed over a surface. 3. Volume Charge Distribution: Charge is distributed throughout a volume. Formula: The electric field due to a continuous charge distribution is calculated using the formula: E = ∫ dE Where:  dE = Electric field due to a small element of charge  Applications:  1. Calculating electric fields: For complex charge distributions. 2. Understanding charge behavior: In various systems, such as capacitors and conductors. Some examples of continuous charge distributions: 1. Uniformly Charged Rod: Calculate the electric field at a point on the axi...
Read more