Ch 22: Gauss's Law Flashcards
What is the general premise of Gauss’s Law?
Given any general distribution of charge, we surround it with an imaginary surface that encloses the charge. Then we look at the electric field at various points on this imaginary surface. Gauss’s Law is a relationship between the field at all the points on the surface and the total charge enclosed within the surface.
A positive charge produces an ___ electric flux.
outward
A negative charge produces an ___ electric flux.
inward
What are the three cases in which there is zero net charge inside a box and no net electric flux through the surface?
1)an empty box w/ no charge inside box, 2) a box containing one positive and one equal-magnitude negative point charge, and 3)an empty box immersed in a uniform electric field
The net electric flux due to a single point charge inside the box is independent of ____ and depends only on ____.
the size of the box; the net charge inside the box
T/F: Charges outside the surface give an electric flux through the surface.
FALSIES
T/F: Doubling the size of the enclosed charge doubles the flux.
QUITE TRUE QUITE TRUE
T/F: Doubling the dimensions of the box doubles the flux.
FALSE
What is the formula for electric flux of a uniform electric field?
Φ = EAcos ϕ
(the dot product of E and A; the portion of the electric field perpendicular to the area
Increasing the area ___(increases/decreases) the flux.
increases
Increasing the electric field ___(increases/decreases) the flux.
increases
What are the units for flux?
1 Nm²/C
What is the formula for flux over a nonuniform electric field?
⌠EcosϕdA; the surface integral of E; this is the average value of the perpendicular component of the electric field, multiplied by the area of the surface
Gauss’s law is completely equivalent to ___.
Coulomb’s law
Gauss’s law states ___.
the total electric flux through any closed surface is proportional to the total/net electric charge inside the surface
What is the magnitude of E at every point on a spherical surface?
1/4πε • q/R²
What is the electrical flux of a spherical surface with a point charge at its center?
q/ε
In an imaginary spherical surface, the flux is independent of ___ and depends only on ___.
the radius R of the sphere; the charge q enclosed by the sphere
T/F: If an irregular surface encloses a charge, the flux through the surface is different from that of a sphere.
FALALALALALALALSE
For a closed surface enclosing no charge, flux is equal to ___.
zero
The total electric flux through a closed surface is equal to ___.
the total/net electric charge inside the surface, divided by ε
Q_encl is equal to ___.
the algebraic sum of all the positive and negative charges enclosed by the Gaussian surface
Outside charges contribute to the total ___ but not the total ___.
electric field; flux
What two questions does Gauss’s Law answer?
If the electric field pattern is known in a given region, what can we determine about the charge distribution in that region? If the charge distribution is known, what can we determine about the electric field that the charge distribution produces?
Gauss’s law is valid for ___.
any distribution of charges and for any closed surface
What are the two ways Gauss’s Law can be used?
1) If we know the charge distribution and if it has enough symmetry to let us evaluate the integral in Gauss’s law, we can find the field or 2) if we know the field we can use Gauss’s law to find the charge distribution, such as charges on conducting surfaces
When excess charge is placed on a solid conductor and is at rest, it resides ___.
entirely on the surface, not in the interior of the material
When is Gauss’s law most useful?
When the charge distribution has spherical, cylindrical, or planar symmetry- the symmetry determines the direction of E
What should be your Gaussian surface for the following charge distributions? a)spherical; b)cylindrical; c)planar
a)concentric spherical surface; b)coaxial cylindrical surface with flat ends perpendicular to the axis of symmetry; c)cylindrical surface w/ flat ends parallel to the plane
A well-chosen Gaussian surface should make integration ___.
trivial or unnecessary
When is E_perp=E=const? What does flux equal for that condition?
When E is perpendicular at every point to a surface with area A, points outward/inward from the interior of the surface, and has the same magnitude at every point on the surface; flux is simply EA if E is outward and -EA if E is inward
When does E_perp=0? What does flux equal for that condition?
When E is tangent to a surface at every point, OR if E=0 at every point; flux = 0
When there is no charge within a Gaussian surface, the field at any given point on the surface is ___. In that case, the total electric flux through the surface is ___.
not necessarily zero; always zero
If an isolated charge q is placed in a cavity in a conductor, the surface of the cavity must have a charge of ___, and the surface of the conductor must have an excess charge of ___.
-q; +q
What makes electrostatic shielding (Faraday cages) possible?
The field of induced charges on the box combines with the uniform field to give zero total field inside the box
If σ is positive, the electric field points ___ and E_perp is ___.
outward; positive
If σ is negative, the electric field points ___ and E_perp is ___.
inward; negative
Using σ, what is the flux and E_perp at the surface of a conductor?
Φ=σA/ϵ and E_perp= σ/ϵ
The field magnitude between 2 infinite flat oppositely charged conducting plates is ___.
σ/ϵ, which is the same at all distances from the plates
