Ch. 23 Gauss' Law

In the figure, an electron is released between two infinite nonconducting sheets that are horizontal and have uniform surface charge densities σ(+) and σ(-), as indicated. The electron is subjected to the following three situations involving surface charge densities and sheet separations. Rank the magnitudes of the electron's acceleration, greatest first.

1 = 2 = 3

In each of the four cases below, the surfaces have the same area Δ𝐴and the electric field is the same as well vector 𝑛 is the direction of the positive normal on the surface. In which case is the flux of the electric field zero?

C. The flux of 𝐸 is 𝐸∙(ΔA vector 𝑛). The angle between the vectors is 90°and the do product is zero. The field vector is tangent to the area and does not go through it.(Lecture 5 for pics)

You put point charge (q) in cavity of conductor with no net charge, what can you say about induced charges?

Consider a gaussian surface inside the conductor that encloses cavity, so the flux would be zero with induced charge on surface of cavity that adds up to charge of q.

10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3 C is placed at the center of the cavity. The net charge on the inner surface of the shell is:

E. The induced charge on the inner surface must be equal and opposite to the charge inside the cavity. So this induced charge is 3 C. The total charge on the shell is 10 C, of which 3 C is on the inner surface. So the outer surface must have 7 C.

A negatively charged particle is placed outside a shell of uniform positive charge. Which describes the force vector on the particle due to the shell?

It is directed toward the center of the shell.

Which describes the vector calculation of the electric flux through a section of a closed surface?

It is the dot product of the electric field and the section's area vector.

We place a closed Gaussian cylinder around a rod with uniform positive charge, coaxial with the rod. Which describes the electric field through the cylinder?

The electric field is outward through the curved side.

A Gaussian sphere is inside a ball of uniform negative charge, concentric with the ball. Which describes the amount of charge enclosed by the Gaussian sphere?

The enclosed charge is proportional to the volume of the Gaussian sphere.

Which describes the electric field of a ball of uniform positive charge?

The field is maximum at the surface and progressively smaller as you move away from the surface, either toward the center or away from the center.

Which describes the electric field outside a charged metal surface?

The field is proportional to the surface charge density.

A negatively charged particle is placed inside (in the hollow of) a shell of uniform negative charge. Which describes the force on the particle due to the shell?

The force is zero.

We bring an electron near a positively charged flat metal sheet. Which describes the surface charge density at the region on the sheet that is closest to the electron?

The presence of the electron increases the magnitude of the surface charge density.

flux

The rate of transfer of material, particle, energy, or fluid within a system per unit of time.

Gauss Law

the total flux summed over any closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space.

The flux of the electric field through any closed surface is proportional to the total __________ by the surface. The constant of proportionality is 1/𝜀0, where 𝜀0 is the permittivity of free space.

charge enclosed (𝑄𝑒𝑛𝑐)

Surface of a Cylinder is __________ surface

closed

We associate vectors with infinite as dA =

dA* normal vector

The flux of E-field though any closed surface is proportional to the total charge _________by surface.

enclosed

Flux of vector J going through plane A, with uniform flow to plane tilted relative to direction of flow.

flux (phi) = vector J *area vector *cos(theta).

a closed boundary doesn't have a boundary and separates into ____ and ____ regions.

inner and outer

The area vector for a flat surface:

is perpendicular to the surface and has a magnitude equal to the area of the surface.

inward flux is __________

negative

In a conductor, charges movie in response to external electric field until _________ left in conductor

no

If you put excess charge on conductor, where does it end up?

on surface of conductor. Choose Gaussian surface just inside conducting material. The flux integral is zero, the electric field everywhere on gaussian is zero, so charge is zero.

curved side by itself is a _________ surface

open

any field parallel to surface will move electrons until not _______.

parallel.

For surface element, the are two normal vectors on each side, and for closed surface the outward direction is ________.

positive

outward flux is _________

positive

uniform flow through a plane to direction of flow.

rate of flow =( Material going through/Area * time ) * area of plane.

an open surface has a boundary, and it does not separate into different _____.

regions

dA

surface element

How can the conductor remain neutral if surface has -q?

the outer surface must have net charge +q

A small charged ball lies within the hollow of a metallic spherical shell of radius R. For three situations, the net charges on the ball and shell, respectively, are (1) +4q, 0; (2) -6q, +10q; (3) +16q, -12q. (a) Rank the situations according to the charge on the inner surface of the shell, most positive first. (b) Rank the situations according to the charge on the outer surface of the shell, most positive first.

A. 2 > 1 > 3 B. 1 = 2 = 3

A surface has the area vector A→= (2i+3j) m2. (a) What is the flux of a uniform electric field through it if the field is E→=⁢ 4i N/C? (b) What is the flux of a uniform electric field through it if the field is E→=4k N/C?

A. 8 N·m2/C B. 0 N·m2/C

In each of the four cases below a Gaussian circle is represented by the dashed line circle and the arrows represent electric field lines. In which of the four cases is the flux through the Gaussian circle not equal to zero?

A. In C and D, flux goes in from one side and comes out the other side. Gauss' law says any field produced by charges outside the Gaussian surface has zero flux. (see lecture 5 for pics)

The figure shows four Gaussian surfaces consisting of identical cylindrical midsections but different end caps. The surfaces are in a uniform electric field E→ that is directed parallel to the central axis of each cylindrical midsection. The end caps have these shapes: S1, convex hemispheres; S2, concave hemispheres; S3, cones; S4, flat disks.(a) Rank the surfaces according to the net electric flux through them, greatest first. (b) Rank the surfaces according to the electric flux through the top end caps, greatest first.

A. S1=S2=S3=S4 B. S1=S2=S3=S4

10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3 C is placed at the center of the cavity. The magnitude of the electric field outside the shell at a distance 𝑟from the center of the shell is:

A. The charges on the inner surface and in the cavity are hidden from the outside world. The field outside is determined entirely by the charges on the outer surface.

A closed cylinder with a 0.15-m radius ends is in a uniform electric field of 300 N/C, perpendicular to the ends. The total flux through the cylinder is:

A. The flux through the curved surface is zero since the filed doesn't pierce this surface. The fluxes through the end are equal and opposite because ehtfiled is the same but normal vectors point in opposite directions.

The figure shows four solid spheres, each with charge Q uniformly distributed through its volume. (a) Rank the spheres according to their volume charge density, greatest first. (b) The figure also shows a point P for each sphere, all at the same distance from the center of the sphere. Rank the spheres according to the magnitude of the electric field they produce at point P, greatest first.

A. a > b > c > d B. a = b > c > d (see Ch. 23 B homework pics)

How is the charge distributed on outer surface?

No field on outer surface, so charge cannot be distributed, exactly as it would if there is no cavity or point charge inside.

Can you put positive and negative charges in different places but keep total zero.

No, any closed surface inside conductor must have zero charge inside.

The figure shows four situations in which four very long rods extend into and out of the page (we see only their cross sections). The value below each cross section gives that particular rod's uniform charge density in microcoulombs per meter. The rods are separated by either d or 2d as drawn, and a central point is shown midway between the inner rods. Rank the situations according to the magnitude of the net electric field at that central point, greatest first.

a > c > b = d

Guass' Law applies to ______ closed surface

any