24. Electric Force & Field; Gauss' Law

Gauss' Law

24. Electric Force & Field; Gauss' Law

Gauss' Law

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Electric Field Within Spherical Conductor

Electric Field due to Hollow Shell

Surface Charge Density

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Anderson Video - Gauss's Law Intro

Anderson Video - Gauss's Law Example

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Physics 37.1 Gauss's Law Understood (2 of 29) What is Electric Flux?

03:48

Physics 37.1 Gauss's Law Understood (2 of 29) What is Electric Flux?

Gauss Law Cylinder, Infinite Line of Charge, Electric Flux & Field, Physics Problems

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Electric Flux and Gauss’s Law | Electronics Basics #6

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Multiple Choice

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

A spherical, thin conducting shell of radius 8cm has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field 4 cm from the center? At 12 cm?

A cube has sides equal to

4.0 cm

. The net flux through the cube is

12 N \cdot m^{2} / C

outward. Is the net charge in the cube positive, negative or zero?

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Multiple Choice

An electric field with strength

3500 N / C

exists just outside a face of a large block of aluminum. If the electric field points towards the block, what is the surface charge density on the face of the block?

4.0 cm

has a charge of

23 nC

evenly distributed throughout the sphere. What is the electric field strength

1.0 cm

from the center of the sphere?

An insulating sphere of radius

4.0 cm

is in the center of a conducting spherical shell with inner radius of

5.0 cm

and outer radius of

7.0 cm

. The insulating sphere has a charge of

- 34 nC

and the conducting spherical shell has a net charge of

42 nC

. What is the total charge on the inner surface of the conducting spherical shell?

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Multiple Choice

A very long insulating cylinder has radius

4.7 cm

. Every

3.0 m

length of the cylinder contains a charge of

86 nC

evenly distributed throughout. What is the strength of the electric field

3.0 cm

from the axis of the cylinder?

474

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Textbook Question

The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

1460

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Textbook Question

The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (a) What is the electric field this nucleus produces just outside its surface?

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate:(c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate: (b) the electric field at the planet's surface (refer to the astronomical data inside the back cover);

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/m2. A charge of −0.500 μC is now introduced at the center of the cavity inside the sphere. (c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?

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Textbook Question

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/m2. A charge of −0.500 μC is now introduced at the center of the cavity inside the sphere. (b) Calculate the strength of the electric field just outside the sphere?

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Textbook Question

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/m2. A charge of −0.500 μC 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?

429

views

Textbook Question

You measure an electric field of 1.25×106 N/C at a distance of 0.150 m from a point charge. There is no other source of electric field in the region other than this point charge. (a) What is the electric flux through the surface of a sphere that has this charge at its center and that has radius 0.150 m? (b) What is the magnitude of this charge?

1989

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Textbook Question

Charge q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E = 940 N/C. What are (b) the electric field at a distance of 2.00 cm from the sphere's center?

The earth has a vertical electric field at the surface, pointing down, that averages 100 N/C. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth?

307

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Textbook Question

An infinite slab of charge of thickness 2𝒵₀ lies in the xy-plane between 𝒵 = -𝒵₀ and 𝒵 = +𝒵₀ . The volume charge density p (C/m³) is a constant. (b) Find an expression for the electric field strength above the slab (𝒵 ≥ 𝒵₀).

476

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Textbook Question

A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R ) is E(r) = r⁴ Eₘₐₓ / R⁴ . (b) Find an expression for the volume charge density ρ(r) inside the ball as a function of r.

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Textbook Question

FIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) 2q / ϵ₀ , (b) q / ϵ₀ , (c) 0, and (d) 5q / ϵ₀ .

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Textbook Question

What is the net electric flux through the cylinder of FIGURE EX24.21?

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Textbook Question

A conductor with an inner cavity, like that shown in Fig. 22.23c, carries a total charge of +5.00 nC. The charge within the cavity, insulated from the conductor, is −6.00 nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?

1296

views

Textbook Question

A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ = 5.00×10−6 C/m2. (a) A small sphere of mass m = 8.00×10−6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (b) What is q if the sphere is released 1.50 cm above the sheet?

334

views

Textbook Question

A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ = 5.00×10−6 C/m2. (a) A small sphere of mass m = 8.00×10−6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (a) If the sphere is to remain motionless when it is released, what must be the value of q?

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views

Textbook Question

An infinitely long cylindrical conductor has radius r and uniform surface charge density σ. (b) In terms of σ, what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis? (c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis.

An infinitely long cylindrical conductor has radius r and uniform surface charge density σ. (a) In terms of σ and R, what is the charge per unit length λ for the cylinder?

A very long conducting tube (hollow cylinder) has inner radius A and outer radius b. It carries charge per unit length +α, where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +α. (a) Calculate the electric field in terms of α and the distance r from the axis of the tube for (i) r < a; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of R.

A very long conducting tube (hollow cylinder) has inner radius A and outer radius b. It carries charge per unit length +α, where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +α. (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?

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Textbook Question

"(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on

(b) the outer surface of the shell?"

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Textbook Question

(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on

(a) the inner surface of the shell and.

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Textbook Question

An infinite cylinder of radius R has a linear charge density λ . The volume charge density (C/m³) within the cylinder (r ≤ R ) is p (r) = rp₀ / R, where p₀ is a constant to be determined. (b) The charge within a small volume dV is dq = p dV. The integral of p dV over a cylinder of length L is the total charge Q = λ L within the cylinder. Use this fact to show that p₀ = 3λ / 2πR² Hint: Let dV be a cylindrical shell of length L, radius r, and thickness dr. What is the volume of such a shell?

269

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Textbook Question

A 20-cm-radius ball is uniformly charged to 80 nC. (b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?

275

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Textbook Question

A proton orbits a long charged wire, making 1.0×10^6 revolutions per second. The radius of the orbit is 1.0 cm. What is the wire's linear charge density?

270

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Textbook Question

CALC A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm) , where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign.

321

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Textbook Question

CALC A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density λ=a|y|, where a is a constant with the units C/m^2. b. Determine the constant a in terms of L and the rod's total charge Q.

365

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Textbook Question

A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ ₀x/L, where x is measured from the rod's left end. a. What is λ₀ in terms of Q and L?

435

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Textbook Question

The electric field is constant over each face of the tetrahedron shown in FIGURE EX24.4. Does the box contain positive charge, negative charge, or no charge? Explain.

116

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Textbook Question

The three parallel planes of charge shown in FIGURE P24.44 have surface charge densities ─ ½ η , η , and ─ ½ η. Find the electric fields EA (→ above E) to ED (→ above E) in regions A to D. The upward direction is the + y-direction.

490

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Textbook Question

Charges q₁ = -4Q and q2 = +2Q are located at 𝓍 = -a and 𝓍 = + a, respectively. What is the net electric flux through a sphere of radius 2a centered (a) at the origin and (b) at 𝓍 = 2a?

257

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Textbook Question

A Geiger counter is used to detect charged particles emitted by radioactive nuclei. It consists of a thin, positively charged central wire of radius Rₐ surrounded by a concentric conducting cylinder of radius Rᵦ with an equal negative charge (Fig. 23–57). The charge per unit length on the inner wire is λ (units C/m) . The interior space between wire and cylinder is filled with low-pressure inert gas. Charged particles ionize some of these gas atoms; the resulting free electrons are attracted toward the positive central wire. If the radial electric field is strong enough, the freed electrons gain enough energy to ionize other atoms, causing an “avalanche” of electrons to strike the central wire, generating an electric “signal.”

(a) Find the expression for the electric field between the wire and the cylinder, and (b) show that the potential difference between Rₐ and Rᵦ is

Vₐ - Vᵦ = ( λ / 2π∊₀ ) ln( Rᵦ/Rₐ) .

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24. Electric Force & Field; Gauss' Law

Gauss' Law

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Learn with other creators

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