Flashcards in Chapter 23 Deck (15):
The electric flux oIo through a surface is the amount of electric field that pierces the surface.
The area vector dA_vector for an area element (patch element) on a surface is a vector that is perpendicular to the element and has a magnitude equal to the area dA of the element.
The electric flux doIo through a patch element with area vector dA_vector is given by a dot product:
doIo = E_vector (dot) dA_vector .
The total flux through a surface is given by oIo = S_integral
E_vector (dot) dA_vector (total flux) where the integration is carried out over the surface.
The net flux through a closed surface (which is used in Gauss’ law) is given by oIo = So_circle_in_integral
E_vector (dot) dA_vector (net flux) where the integration is carried out over the entire surface.
Gauss’ law relates the net flux oIo penetrating a closed surface to the net charge q_enc enclosed by the surface:
E0*oIo = q_enc (Gauss’ law).
Gauss’ law can also be written in terms of the electric field piercing the enclosing Gaussian surface: E0*So_circle_in_integral
E_vector (dot) dA_vector (net flux) = q_enc (Gauss’ law).
An excess charge on an isolated conductor is located entirely on the outer surface of the conductor.
The internal electric field of a charged, isolated conductor is zero, and the external field (at nearby points) is perpendicular to the surface and has a magnitude that depends on the surface charge density o-: E = o- / E0
The electric field at a point near an infinite line of charge (or charged rod) with uniform linear charge density lambda is perpendicular to the line and has magnitude
E = lambda / 2*pi*E0*r (line of charge),
where r is the perpendicular distance from the line to the point.
The electric field due to an infinite nonconducting sheet with uniform surface charge density o- is perpendicular to the plane of the sheet and has magnitude
E = o- / 2*E0 (nonconducting sheet of charge).
he external electric field just outside the surface of an isolated charged conductor with surface charge density o- is perpendicular to the surface and has magnitude
E = o- / E0 (external, charged conductor).
Inside the conductor, the electric field is zero.
Outside a spherical shell of uniform charge q, the electric field due to the shell is radial (inward or outward, depending on the sign of the charge) and has the magnitude
E = (1 / 4*pi*E0) * (q / r^2) (outside spherical shell),
where r is the distance to the point of measurement from the center of the shell. The field is the same as though all of the charge is concentrated as a particle at the center of the shell.
Inside the shell, the field due to the shell is zero.