Coulomb’s Law and Electric Field
– Coulomb’s law states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
– The force can be attractive or repulsive depending on the charges of the objects.
– The magnitude of the force is given by the equation F = (1/4πε₀)(qQ/r²), where ε₀ is the vacuum permittivity.
– The SI unit for charge is coulombs (C) and for distance is meters (m).
– The Coulomb constant is approximately 8.987551792 x 10^9 N·m²/C².
– The electric field is a vector field that represents the force experienced by a hypothetical test charge at a given point.
– It is defined as the electrostatic force divided by the charge of the test charge.
– Electric field lines are useful for visualizing the direction and magnitude of the electric field.
– The divergence of the electric field is related to the charge density through Gauss’s law.
– Electric field lines start from positive charges and end on negative charges.
Poisson and Laplace Equations
– Poisson’s equation relates the electrostatic potential to the charge density.
– In the absence of unpaired electric charge, the equation becomes Laplace’s equation.
– These equations are used to solve for the electrostatic potential in different scenarios.
– Poisson’s equation is written as ∇²Φ = -ρ/ε₀, where Φ is the potential and ρ is the charge density.
– Laplace’s equation is written as ∇²Φ = 0, where Φ is the potential.
Electrostatic Approximation
– The electrostatic approximation assumes that the electric field is irrotational, meaning ∇ × E = 0.
– This assumption implies the absence or near-absence of time-varying magnetic fields.
– Electrostatics does not require the absence of magnetic fields or electric currents, but they must not change with time or change very slowly.
– In some cases, both electrostatics and magnetostatics are needed for accurate predictions.
– Electrostatics and magnetostatics are non-relativistic limits of electromagnetism.
Electrostatic Potential
– The electric field can be expressed as the gradient of the electrostatic potential.
– The electrostatic potential is a scalar function that represents the amount of work per unit charge required to move a charge between two points.
– Electric potential is constant in regions where the electric field vanishes.
– The electric potential can be calculated using the equation ∇Φ = -E.
– The electric potential due to multiple point charges can be obtained by summing the contributions from each charge.
Electrostatic Pressure and Electromagnetism
– A surface charge on a conductor experiences a force in the presence of an electric field.
– The force is the average of the discontinuous electric field at the surface charge.
– The average force in terms of the field just outside the surface is given by the equation P = (ε0/2)E^2.
– This pressure tends to draw the conductor into the field.
– The pressure is independent of the sign of the surface charge.
– Electromagnetism is the fundamental interaction between charged particles.
– Electrostatics is a branch of electromagnetism that deals with stationary charges.
– Electromagnetic generators are machines that create static electricity.
– Electrostatic induction is the separation of charges due to electric fields.
– Permittivity and relative permittivity describe the electric polarizability of materials. Source: https://en.wikipedia.org/wiki/Electrostatic
Electrostatics is a branch of physics that studies slow-moving or stationary electric charges.
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ἤλεκτρον (ḗlektron), was thus the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law.
There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier and laser printer operation. Electrostatic forces play a large role at the nanoscale; for instance, the force between an electron and a proton, which together make up a hydrogen atom, is more than 39 orders of magnitude stronger than the gravitational force acting between them. Because they are large at small scales, Coulomb forces between electrons and the positively charged nuclei play a very large role in how atoms and molecules behave.
