Practice: Rank the flux through surfaces A, B and C in the figure below from greatest to smallest.

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Practice: Rank the flux through surfaces A, B and C in the figure below from greatest to smallest.

Practice: A spherical, conducting shell has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field at 4 cm? At 12 cm?

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If more electric field lines leave a gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?
A) is positive
B) is negative
C) is zero
D) depends

A negative charge (-Q) resides at the center of a pyramid with a triangular base. The electric flux through each of the surface is
A) -Q/(4ε0)
B) Q/(4ε0)
C) -Q/ε0
D) Q/ε0

A solid conducting sphere of radius R1 and total charge q1 is enclosed by a conducting shell with an inner radius R2 and outer radius R3 and total charge q2. OA = a and OC = c.

Some shape is made up of 8 different surfaces. If the electric flux through each surface of the shape is given below, how much charge is enclosed by this shape?
Φ1 = 50 Nm2/C Φ2 = 75 Nm2/C
Φ3 = -150 Nm2/C Φ4 = 0 Nm2/C
Φ5 = -45 Nm2/C Φ6 = 150 Nm2/C
Φ7 = 100 Nm2/C Φ8 = -125 Nm2/C

A (4.15 m by 4.15 m) square base pyramid with height of 2.53 m is placed in a vertical electric field of 50.1 N/C. Calculate the total electric flux which goes out through the pyramid’s four slanted surfaces.

A spherical surface completely surrounds two charges. Find the electric flux through the surface if the charges are +3.5x10-6 C and -2.3x10-6 C.

A solid conducting sphere of radius a is placed inside of a conducting shell which has an inner radius b and an outer radius c. There is a charge q1 on the sphere and a charge q2 on the shell.

A cubic box of side a, oriented as shown, contains an unknown charge. The vertically directed electric field has a uniform magnitude E at the top surface and 2 E at the bottom surface.

A point charge 4q > 0 is placed at the center point O. There is a thick conducting spherical shell with inner radius R2 and outer radius R '2 centered at O. The thickness of this shell is R '2 − R2. Another larger thin concentric spherical shell has radius R3. The thickness of this shell is negligible. The thick shell is charged with a charge 3q and the large thin shell is charged with a charge 9q.

A point charge 4q > 0 is placed at the center point O. There is a thick conducting spherical shell with inner radius R2 and outer radius R '2 centered at O. The thickness of this shell is R '2 − R2. Another larger thin concentric spherical shell has radius R3. The thickness of this shell is negligible. The thick shell is charged with a charge 3q and the large thin shell is charged with a charge 9q.

The net electric flux through a closed surface is
1. zero if only positive charges are enclosed by the surface.
2. zero if only negative charges are enclosed by the surface.
3. infinite only if the net charge enclosed by the surface if zero.
4. zero if the net charge enclosed by the surface is zero.
5. infinite only if there are no charges enclosed by the surface.

The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them? (Check all that apply).(a) d(b) a(c) b(d) c

A charge of 10 μC is at the geometric center of a cube. What is the electric flux through one of the faces? The permittivity of a vacuum is 8.85419 × 10−12 C2/N • m2 .
1. 353882.0
2. 171294.0
3. 201411.0
4. 188235.0
5. 116706.0
6. 225882.0
7. 165647.0
8. 263529.0
9. 327529.0
10. 297411.0

A solid conducting sphere of radius R1 and total charge q1 is enclosed by a conducting shell with an inner radius R2 and outer radius R3 and total charge q2. OA = a and OC = c.

A spherical shell has an inner radius of 10 cm and an outer radius of 12 cm. If the spherical shell has a charge Q = 10 nC, and encloses a charge q = -7 nC, what is the surface charge density on the inner surface of the spherical shell?

A point charge Q is placed at the center of a cube of side a. The electric flux through any one of the six sides is
a) kQ/a2
b) Q/6ϵ0
c) Q/ϵ0
d) 0
e) can not be determined from the informations provided.

The electric field is constant over each face of the cube shown in the figure. Does the box contain positive charge, negative charge, or no charge?
a) Positive charge
b) Negative charge
c) No charge

A point charge Q is placed at the center of cube of side a. The electric flux through any one of the six sides is
kQ/a2
Q/6εo
Q/εo
0
Cannot be determined from the information provided

A charge is placed in a closed box. If the size of the box doubles, the electric flux going through the boxA) reverse the sign but keeps the same magnitude.B) keeps the same.C) doubles.D) is only half of the original flux.

Gaussian surface A is a cube with side length L and encloses a charge Q. A separate gaussian surface B is a sphere with radius length 10L and encloses a charge Q/2. What is the ratio between the electric fluxes, ΦEA / ΦEB, for these two surfaces?
A. 200π/3
B. 3/(200π)
C. 2/1
D. 1/1

A conducting spherical shell carrying a charge -5 nC encloses a point charge +5 nC. What is the induced charge (qout) on the "outer" surface of the conducting shell?a. zerob. +5 nCc. -5 nCd. +10 nCe. -10 nC

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.Now a second charge, q2, is brought near the outside of the conductor. Which of the following quantities would change?(a) The total surface charge on the wall of the cavity, qint.would changewould not change(b) The total surface charge on the exterior of the conductor, qext.would changewould not change

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.(a) What is the total surface charge qint on the interior surface of the conductor (i.e., on the wall of the cavity)? (b) What is the total surface charge qext on the exterior surface of the conductor?(c) What is the magnitude Eint of the electric field inside the cavity as a function of the distance r from the point charge?

A hollow conducting sphere of radius R carries a negative charge -q. (a) Write expressions for the electric field E inside (r<R) and outside (r>R) the sphere. Also indicate the direction of the field. (b) Sketch a Graph of the field strength as a function of r.

To understand the meaning of the variables in Gauss's law, and the conditions under which the law is applicable.Gauss's law is usually writtenwhere ε0 = 8.85 x 10-12 C2/(N • m2) is the permittivity of vacuum.How should the integral in Gauss's law be evaluated?a) around the perimeter of a closed loopb) over the surface bounded by a closed loopc) over a closed surface

A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37×10−6 C/m2A charge of −0.500μC is now introduced at the center of the cavity inside the sphere. (a) What is the new charge density on the outside of the sphere? (b) Calculate the strength of the electric field just outside the sphere. (c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?

Which spherical Gaussian surface has the larger electric flux?a. Surface Ab. Surface Bc. They have the same flux

a) What is the electric flux Φ3 through the annular ring, surface 3? (Express your answer in terms of C, r1, r2, and any constants.)b) What is the electric flux Φ1 through surface 1? (Express Φ1 in terms of C, r1, r2, and any needed constants.)c) What is the electric flux Φ2 passing outward through surface 2? (Express Φ2 in terms of C, r1, r2, and any constants or other known quantities.)

A cube has one corner at the origin and the opposite cornerat the point (L,L,L). The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by E = (a + bx) x̂ + c ŷ.Find the total electric flux ΦE through the surface of the cube. Express your answer in terms of a,b,c and L. What is the net charge q inside the cube? Express your answer in terms of a, b, c, L, and ϵ0.

A very long, uniformly charged cylinder has radius R and linear charge density λ.a. Find the cylinder's electric field strength outside the cylinder, r ≥ R. Give your answer as a multiple of λ/ε0.Express your answer in terms of some or all of the variables R, r, and the constant π.b. Find the cylinder's electric field strength inside the cylinder, r ≤ R. Give your answer as a multiple of λ/ε0.Express your answer in terms of some or all of the variables R, r, and the constant π.

An infinite cylindrical rod has a uniform volume charge density rho (where ρ > 0). The cross section of the rod has radius r0. 1. Find the magnitude of the electric field E at a distance r from the axis of the rod. Assume that r < r02. In which direction is the electric field on the cylindrical gaussian surface?A. perpendicular to the curved wall of the cylindrical Gaussian surface B. tangential to the curved wall of the cylindrical Gaussian surface C. perpendicular to the flat end caps of the cylindrical Gaussian surface D. tangential to the flat end caps of the cylindrical Gaussian surface

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. Thus, the charge can be considered to be distributed uniformly throughout the cloud. For the purposes of this problem, take the cloud to be a sphere of diameter 1.00km. The point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. This breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. The ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. In addition, the large current will heat up the air, resulting in its rapid expansion. These two phenomena account for the appearance of lightning and the sound of thunder. Take the breakdown electric field of air to be Eb = 3.00 x 106 N/C.Q:Estimate the total charge q on the cloud when the breakdown of the surrounding air is reached.Express your answer numerically, to three significant figures, using ε0 = 8.85 x 10-12 C2/(N•m2). A: in terms of Coulombs

Consider a point charge g in three-dimensional space. Symmetry requires the electric field to point directly away from the charge in all directions. To find E(r), the magnitude of the field at distance r from the charge, the logical Gaussian surface is a sphere centered at the charge. The electric field is normal to the surface, so the dot product of the electric field and an infinitesimal surface element involves element involves cos(0) = 1. The flux integral is therefore reduced to , where E(r) is the magnitude of the electric field on the Gaussian surface, and A(r) is the area of the surface. Part ADetermine the magnitude E(r) by apliying Gauss's law. Part BBy symmetry, the electric field must point radially outward from the wire at each point; that is , the field lines lie in planes perpendicular to the wire. In solving for the magnitude of the radial electric field E(r) produced by a line charge with charge density λ, one should use a cylindrical Gaussian surfase whose axis is the line charge. The lenght of the cylindrical surface L should cancel out of the expression for E(r). Apply Gauss's law to this situation to find an expression for E(r). Part CIn solving for the magnitude of the electric field E(z) produced by a sheet charge with charge density δ, use the planar symmetry since the charge distribution doesn't change if you slide it in any direction of xy plane parallel to the sheet. Therefore at each point, the electric field is perpendicular to the sheet and must have the same magnitude at any given distance on either side of the sheet. To take advantage of these symmetry properties, use a Gaussian surface in the shape of a cylinder with its axis perpendicular to the sheet of charge, with ends of area A which wil cancel out the expression for E(z) in the end. The result of applying Gauss's law to this situation then gives an expression for E(z) for both z>0 and z<0.

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.Now a second charge, q2, is brought near the outside of the conductor. Which of the following quantities would change?(a) The electric cavity within the cavity, Ecav.would changewould not change(b) The electric field outside the conductor, Eext.would changewould not change

An insulating sphere of radius a, centered at the origin, has a uniform volume charge density.Find the electric field E(r) inside the sphere (for r< a) in terms of the position vector r .Express your answer in terms of r and ρ

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.What is the electric field E_ext outside the conductor?(a) Zero(b) The same as the field produced by a point charge q located at the center of the sphere.(c) The same as the field produced by a point charge located at the position of the charge in the cavity.

A slab of insulating material of uniform thickness d, lying between -d/2 to +d/2 along the x axis, extends infinitely in the y and z directions. The slab has a uniform charge density ρ. The electric field is zero in the middle of the slab, at x = 0.A. What is Eout, the magnitude of the electric field outside the slab? As implied by the fact that Eout is not given as a function of x this magnitude is constant everywhere outside the slab, not just at the surface. Express your answer in terms of d, ρ, and ε0.B. What is Ein, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, ρ, and ε0.

A net charge is placed on a hollow conducting sphere. How does the net charge distribute itself?A. The net charge uniformly distributes itself on the sphere's inner surface.B. The net charge uniformly distributes itself on the sphere's inner and outer surfaces.C. The net charge uniformly distributes itself on the sphere's outer surface.D. The net charge uniformly distributes itself throughout the thickness of the conducting sphere.E. The net charge clumps together at some location within the sphere.

(Figure 1) shows two very large slabs of metal that are parallel and distance l apart. The top and bottom surface of each slab has surface area A. The thickness of each slab is so small in comparison to its lateral dimensions that the surface area around the sides is negligible. Metal 1 has total charge Q1=Q and metal 2 has total .A) Determine the surface charge density ηa on the surface a. Give your answer as a multiple of Q/A.B) Determine the surface charge density ηb on the surface b. Give your answer as a multiple of Q/A.C) Determine the surface charge density ηc on the surface c. Give your answer as a multiple of Q/A.D) Determine the surface charge density ηd on the surface d. Give your answer as a multiple of Q/A.

The Sun is lower in the sky during the winter than it is during the summer.a.) How does this change affect the flux of sunlight hitting a given area on the surface of the Earth?b.) How does this change affect the weather?

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