EP 2 - Lecture 2
What is Gaussian surface?
A closed surface of arbitrary shape centered around a point charge.
How to obtain the electric field when we know the electric potential?
Differentiation of the electric potential.
How to relate the divergence of the electric field to the local charge density and what is the Laplace operator?
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2 (where ∇ is the nabla operator) or Δ.
Electric potential of a point charge, properties of electric potential?
In this case only the r component enters the integral (see image) - The electric potential of a point charge depends only on the radius. - The potential increase as the charge gets closer to the center of the electric field. (3D plot of the potential energy, where the high is the potential itself.) (Points of equal height correspond to positions of constant potential, such that no energy would be needed/released when the charge is moving along these positions)
What is Electric Potential?
It represents the work that is required to move our object/charge in the force field. In analogy to the electric field we define the electric potential with respect to a zero potential reference point r0, with V(r0) = 0 Often, we choose 𝑟0 = ∞, since at infinite distance the electrostatic force is vanishing. The unit of the potential is the volt: [V] = 1 Nm/(As) = 1 VAs/As = 1 V.
More about divergence theorem and Gauss law.
The divergence div(E) provides hereby the local field line increase or decrease! Watch out: div(E) = 0 does not mean that the field is constant. The divergence only denotes an absolute field change non-depending on the direction. div(E) = 0 can thus also be obtained by a field decrease in one but a field increase in another direction, such as for a field that turns or diverges.
Basic Statement of the divergence theorem?
The divergence theorem is a mathematical statement that these 2 are eual. (Further information later)
What is Electric Flux?
The measure of the flow of the electric field through a given area. It represents the total electric lines crossing the surface in a direction normal to the surface. It is a scalar. It is also proportional to the strength of the electric field. [Nm^2/C]
What is Gauss Law? Electric Flux dependencies?
The net electric flux through any Gaussian surface equals the enclosed charge devided by the dielectric constant.
Correlation between the flux and a sphere's radious? Electrix flux of a sphere with a charge in its center?
This is analogous to a mass current in hydrodynamics. Imagine a mass release in the center of a sphere that moves in all directions outwards. Through any spherical shell the same mass would pass (in steady state) independent of its radius. Similarly, one can imagine photons emitted from a source in vacuum. Here, the photon current given as the intensity times the area of a closed surface would be a constant.
What is the difference between Electric Field and Electric potential (and -U)?
To be answered...
What is Voltage U?
Voltage is the negative potential energy difference between two points.
Equipotential surfaces for two opposite charges?
in vacuum (where we have no polarization of matter etc) the electric potential of multiple static charges can be obtained from the sum of the individual potentials, since the electric field is additive and the potential is just an integral over the sum of the individual fields
What is poison equation?
p is local charge density.
