Ch 22: Gauss's Law

Question 1

What is the general premise of Gauss’s Law?

Answer 1

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.

Question 2

A positive charge produces an ___ electric flux.

Answer 2

outward

Question 3

A negative charge produces an ___ electric flux.

Answer 3

inward

Question 4

What are the three cases in which there is zero net charge inside a box and no net electric flux through the surface?

Answer 4

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

Question 5

The net electric flux due to a single point charge inside the box is independent of ____ and depends only on ____.

Answer 5

the size of the box; the net charge inside the box

Question 6

T/F: Charges outside the surface give an electric flux through the surface.

Answer 6

FALSIES

Question 7

T/F: Doubling the size of the enclosed charge doubles the flux.

Answer 7

QUITE TRUE QUITE TRUE

Question 8

T/F: Doubling the dimensions of the box doubles the flux.

Answer 8

FALSE

Question 9

What is the formula for electric flux of a uniform electric field?

Answer 9

Φ = EAcos ϕ

(the dot product of E and A; the portion of the electric field perpendicular to the area

Question 10

Increasing the area ___(increases/decreases) the flux.

Answer 10

increases

Question 11

Increasing the electric field ___(increases/decreases) the flux.

Answer 11

increases

Question 12

What are the units for flux?

Answer 12

1 Nm²/C

Question 13

What is the formula for flux over a nonuniform electric field?

Answer 13

⌠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

Question 14

Gauss’s law is completely equivalent to ___.

Answer 14

Coulomb’s law

Question 15

Gauss’s law states ___.

Answer 15

the total electric flux through any closed surface is proportional to the total/net electric charge inside the surface

Question 16

What is the magnitude of E at every point on a spherical surface?

Answer 16

1/4πε • q/R²

Question 17

What is the electrical flux of a spherical surface with a point charge at its center?

Answer 17

q/ε

Question 18

In an imaginary spherical surface, the flux is independent of ___ and depends only on ___.

Answer 18

the radius R of the sphere; the charge q enclosed by the sphere

Question 19

T/F: If an irregular surface encloses a charge, the flux through the surface is different from that of a sphere.

Answer 19

FALALALALALALALSE

Question 20

For a closed surface enclosing no charge, flux is equal to ___.

Answer 20

zero

Question 21

The total electric flux through a closed surface is equal to ___.

Answer 21

the total/net electric charge inside the surface, divided by ε

Question 22

Q_encl is equal to ___.

Answer 22

the algebraic sum of all the positive and negative charges enclosed by the Gaussian surface

Question 23

Outside charges contribute to the total ___ but not the total ___.

Answer 23

electric field; flux

Question 24

What two questions does Gauss’s Law answer?

Answer 24

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?

Question 25

Gauss’s law is valid for ___.

Answer 25

any distribution of charges and for any closed surface

Question 26

What are the two ways Gauss’s Law can be used?

Answer 26

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

Question 27

When excess charge is placed on a solid conductor and is at rest, it resides ___.

Answer 27

entirely on the surface, not in the interior of the material

Question 28

When is Gauss’s law most useful?

Answer 28

When the charge distribution has spherical, cylindrical, or planar symmetry- the symmetry determines the direction of E

Question 29

What should be your Gaussian surface for the following charge distributions? a)spherical; b)cylindrical; c)planar

Answer 29

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

Question 30

A well-chosen Gaussian surface should make integration ___.

Answer 30

trivial or unnecessary

Question 31

When is E_perp=E=const? What does flux equal for that condition?

Answer 31

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

Question 32

When does E_perp=0? What does flux equal for that condition?

Answer 32

When E is tangent to a surface at every point, OR if E=0 at every point; flux = 0

Question 33

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 ___.

Answer 33

not necessarily zero; always zero

Question 34

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 ___.

Answer 34

-q; +q

Question 35

What makes electrostatic shielding (Faraday cages) possible?

Answer 35

The field of induced charges on the box combines with the uniform field to give zero total field inside the box

Question 36

If σ is positive, the electric field points ___ and E_perp is ___.

Answer 36

outward; positive

Question 37

If σ is negative, the electric field points ___ and E_perp is ___.

Answer 37

inward; negative

Question 38

Using σ, what is the flux and E_perp at the surface of a conductor?

Answer 38

Φ=σA/ϵ and E_perp= σ/ϵ

Question 39

The field magnitude between 2 infinite flat oppositely charged conducting plates is ___.

Answer 39

σ/ϵ, which is the same at all distances from the plates