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{{Chapter 21Chapter 21

Electric Fields and Dipoles (cont.)Electric Fields and Dipoles (cont.)

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Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same negative charge (–q). There is nothing at point P.

The net electric field that charges #1 and #2 produce at point P is in

Q21.7

Charge #1

Charge #2

–q

–qx

y

P

A. the +x-direction. B. the –x-direction.

C. the +y-direction. D. the –y-direction.

E. none of the above

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Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same negative charge (–q). There is nothing at point P.

The net electric field that charges #1 and #2 produce at point P is in

A21.7

A. the +x-direction. B. the –x-direction.

C. the +y-direction. D. the –y-direction.

E. none of the above

Charge #1

Charge #2

–q

–qx

y

P

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Q21.9

A. the +x-direction.

B. the –x-direction.

C. the +y-direction.

D. the –y-direction.

E. none of the above

Positive charge is uniformly distributed around a semicircle. The electric field that this charge produces at the center of curvature P is in

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A21.9

Positive charge is uniformly distributed around a semicircle. The electric field that this charge produces at the center of curvature P is in

A. the +x-direction.

B. the –x-direction.

C. the +y-direction.

D. the –y-direction.

E. none of the above

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Q21.10

Charge #1

Charge #2

Charge #3

+q

+q

–qx

y

A. clockwise.

B. counterclockwise.

C. zero.

D. not enough information given to decide

Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole.

The net electric torque that charge #1 exerts on the dipole is

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A21.10

A. clockwise.

B. counterclockwise.

C. zero.

D. not enough information given to decide

Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole.

The net electric torque that charge #1 exerts on the dipole is

Charge #1

Charge #2

Charge #3

+q

+q

–qx

y

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Q21.11

Charge #1

Charge #2

Charge #3

+q

+q

–qx

y

A. the +x-direction. B. the –x-direction.

C. the +y-direction. D. the –y-direction.

E. none of the above

Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole.

The net electric force that charge #1 exerts on the dipole is in

© 2012 Pearson Education, Inc.

A21.11

Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole.

The net electric force that charge #1 exerts on the dipole is in

A. the +x-direction. B. the –x-direction.

C. the +y-direction. D. the –y-direction.

E. none of the above

Charge #1

Charge #2

Charge #3

+q

+q

–qx

y

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{{Chapter 22Chapter 22

Gauss’s LawGauss’s Law

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Gauss’s LawGauss’s Law• Gauss’s law is an alternative to Coulomb’s law and is Gauss’s law is an alternative to Coulomb’s law and is

completely equivalent to it.completely equivalent to it.• Carl Friedrich Gauss, shown below, formulated this Carl Friedrich Gauss, shown below, formulated this

law.law.

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Charge and electric fluxCharge and electric flux

Positive charge within the box produces outward Positive charge within the box produces outward electric fluxelectric flux through the surface of the box, and negative charge produces through the surface of the box, and negative charge produces inward flux. (See Figure 22.2 below.)inward flux. (See Figure 22.2 below.)

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Zero net charge inside a boxZero net charge inside a box

Figure below shows three cases in which there Figure below shows three cases in which there is zero is zero netnet charge inside a box and no net charge inside a box and no net electric flux through the surface of the boxelectric flux through the surface of the box..

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What affects the flux through a box?What affects the flux through a box?

As Figure below shows, doubling the charge within the box As Figure below shows, doubling the charge within the box doubles the flux, but doubling the size of the box does not doubles the flux, but doubling the size of the box does not change the flux.change the flux.

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Calculating electric fluxCalculating electric flux

Electric Flux Through a Rectangular SurfaceElectric Flux Through a Rectangular Surface

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Electric flux through a diskElectric flux through a disk

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Electric flux through a cubeElectric flux through a cube

• Evaluate total Electric Flux through cube.Evaluate total Electric Flux through cube.

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Electric flux through a sphereElectric flux through a sphere

• Calculate total Flux due to point charge.Calculate total Flux due to point charge.

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Point charge centered in a spherical surfacePoint charge centered in a spherical surface• The flux through the The flux through the

sphere is independent sphere is independent of the size of the of the size of the sphere and depends sphere and depends only on the charge only on the charge inside. Figure at the inside. Figure at the right illustrates this right illustrates this fact.fact.

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Point charge inside a nonspherical Point charge inside a nonspherical surfacesurface

• As before, the flux is independent of the surface and depends As before, the flux is independent of the surface and depends only on the charge inside. (See Figure 22.12 below.)only on the charge inside. (See Figure 22.12 below.)

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Positive and negative fluxPositive and negative flux

• Figure 22.14 below shows that flux is Figure 22.14 below shows that flux is positive if the enclosed charge is positive, positive if the enclosed charge is positive, and negative if the charge is negative.and negative if the charge is negative.

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A spherical Gaussian surface (#1) encloses and is centered on a point charge +q. A second spherical Gaussian surface (#2) of the same size also encloses the charge but is not centered on it.

Compared to the electric flux through surface #1, the flux through surface #2 is

A. greater.

B. the same.

C. less, but not zero.

D. zero.

E. not enough information given to decide

Q22.1

+q

Gaussian surface #1

Gaussian surface #2

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A spherical Gaussian surface (#1) encloses and is centered on a point charge +q. A second spherical Gaussian surface (#2) of the same size also encloses the charge but is not centered on it.

Compared to the electric flux through surface #1, the flux through surface #2 is

A. greater.

B. the same.

C. less, but not zero.

D. zero.

E. not enough information given to decide

A22.1

+q

Gaussian surface #1

Gaussian surface #2

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Using Gauss’s lawUsing Gauss’s law

• What is the total Flux through the What is the total Flux through the surfaces A,B,C, and D shown below? surfaces A,B,C, and D shown below? iClickers…iClickers…

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Two point charges, +q (in red) and –q (in blue), are arranged as shown.

Through which closed surface(s) is the net electric flux equal to zero?

Q22.2

A. Only surface A

B. Only surface B

C. Only surface C

D. Only surface D

E. Both surface C and surface D

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Two point charges, +q (in red) and –q (in blue), are arranged as shown.

Through which closed surface(s) is the net electric flux equal to zero?

A22.2

A. Only surface A

B. Only surface B

C. Only surface C

D. Only surface D

E. Both surface C and surface D