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Name: Lab Day/Time:

Homework 3 Field Maps

Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiple- choice answers must be circled. In the space after the problem, a short justification of each multiple-choice the answer must be included. The open-response answers must be worked out clearly using good physics presentation and will be graded on correctness and how carefully the work is explained. The problems should be worked in the space after the problem on the assignment printout; additional paper may be used if needed. No credit will be given for answers without appropriate supporting work. Minimum good presentation requires the following: (1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3) Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5) Enough English description to allow the reader to have some idea what you are doing without looking at the math.

Early Questions

The questions in this section are over material that will be covered by Friday. These may be worked before the other questions.

Homework Problem 3.1 A negatively charged pith ball is sus- pended by a string between two equally, but oppositely charged plates. In what direction will the pith ball swing when released?

Select One of the Following:

(a) The ball will swing to the right.

(b) The ball will swing to the left.

(c) The ball will not swing at all.

_

-Q

+

+

+

+

+ _

_

_

_

_

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Homework Problem 3.2 The figure to the right shows an object with charge +2Q and an object with charge −Q. If four field lines exit a +Q charge, how many field lines pass through the dashed surface?

Select One of the Following:

(a) zero lines

(b) two lines

(c) four lines

(d) eight lines

(e) sixteen lines

+2Q -Q

Homework Problem 3.3 Select the one of the following that best describes the relationship between the direction of an electric field line and the velocity of a positively charged particle.

Select One of the Following:

(a) The velocity must ALWAYS be perpendicular to the electric field lines.

(b) The velocity must ALWAYS be in the direction of the electric field lines.

(c) The velocity can be, but is not limited to, the same direction as the field lines.

(d) The velocity will NEVER be in the direction of the electric field line.

(e) The velocity will always be opposite the direction of the electric field line.

Homework Problem 3.4 The figure to the right shows an electric dipole placed in an electric field. Which of the following best describes the dipole’s initial motion if it is fixed to pivot about its center?

Select One of the Following:

(a) rotates clockwise

(b) rotates counterclockwise

+

_

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Homework Problem 3.5 Two electric dipoles are oriented so their moments are aligned with(point in the same direction as) the y-axis and their centers lie on the y-axis. Is the force between the dipoles attractive, repulsive, or zero?

Select One of the Following:

(a) attractive

(b) repulsive

(c) zero

Homework Problem 3.6 A spherical balloon has a surface charge density of σ on its outer surface and has radius a. What is the electric field outside the balloon at all points in space?

Select One of the Following:

(a) σ

ε0 r̂

(b) aσ

ε0r r̂

(c) a2σ

ε0r2 r̂

(d) σ

4πε0r2 r̂

(e) 0

Homework Problem 3.7 What relative orientation must two vectors ~A and ~B have so that the dot-product is maximum?

Select One of the Following:

(a) The vectors must point in the same direction.

(b) The vectors must point in opposite directions.

(c) The vectors must be perpendicular.

(d) The angle between the vectors must be 45◦.

(e) The angle between the vectors does not affect the value of the dot product.

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Homework Problem 3.8 A closed surface has zero net electric flux exiting the surface. Is the electric field necessarily zero at all points on the surface?

Select One of the Following:

(a) yes

(b) no

Homework Problem 3.9 A cube has a uniform electric field normal to all six faces. The strength of the field is 6N C

outward on face 1, 6N C

outward on face 2, 3N C

inward on face 3, 6N C

outward on face 4, 6N C

inward on face 5,

and 10N C

inward on face 6. Does the cube contain a net charge? If it does, what is the sign of the net charge in the cube?

Select One of the Following:

(a) positive

(b) negative

(c) The net charge in the cube is zero.

Homework Problem 3.10 The world’s largest Van de Graaff generator produces an electric field of 4.4× 105 N C

using an electrode that is a sphere of radius 4.5m. How much total charge must be on the surface of the sphere to produce this field?

Select One of the Following:

(a) 2.2× 10−4C

(b) 9.9× 10−4C

(c) 4.5× 10−3C

(d) 3.2× 10−2C

(e) 1.1× 10−1C

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Homework Problem 3.11 The figures below show two concentric spherical shells. The inner shell has total charge −Q and the outer shell +Q. Select the figure that correctly represents the electric field of the system.

Select One of the Following:

(a) Figure (a) (b) Figure (b) (c) Figure (c) (d) Figure (d) (e) Figure (e) (f) Figure (f)

Figure (a) Figure (b) Figure (c)

Figure (d) Figure (e) Figure (f)

Homework Problem 3.12 A hula hoop of radius 1.0m is in a uniform electric field with magnitude 1.0× 102 N C .

Its normal is perpendicular to the field (careful here). What is the flux through the hoop?

Select One of the Following:

(a) 310N C m2

(b) 620N C m2

(c) 1.0× 102 N C m2

(d) 0

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Homework Problem 3.13 A 20cm radius sphere is filled with a uniform volume charge density 3.2×10−6C/m3. Calculate the electric flux out of the surface of the sphere.

Select One of the Following:

(a) 12, 000Nm2/C

(b) 36, 000Nm2/C

(c) 60, 000Nm2/C

(d) 180, 000Nm2/C

(e) 260, 000Nm2/C

Homework Problem 3.14 The figure to the right shows two charged spherical shells. The inner shell has radius a and charge density σa = −σ. The outer shell has radius b and charge density σb = +2σ. Calculate electric field at points in Region I inside the inner shell, at a radius of r < a.

Select One of the Following:

(a) 0

(b) − σ

4πε0r2 r̂

(c) + σ

4πε0r2 r̂

(d) − 4πa2σ

4πε0r2 r̂

(e) + 4πa2σ

4πε0r2 r̂

(f) −4πa2σ + 8πb2σ

4πε0r2 r̂

a

x

y

b

Air

Air

Air

I

II

III

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Homework Problem 3.15 An electric dipole is located at the center of each of the following figures. Which of the field maps drawn below best represents the field of the dipole if the dipole moment points to the top of the page?

Select One of the Following:

(a) Figure (a) (b) Figure (b) (c) Figure (c) (d) Figure (d)

Figure (a) Figure (b)

Figure (c) Figure (d)

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Open Response Questions

All questions in this section must be worked. One of the questions will be graded.

Homework Problem 3.16 Draw the electric field map for four charges arranged in a square. Three of the charges are +q and one is −q. Select four points on the map and draw the direction and relative magnitude of the electric field at each point. Read this information from your map.

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Homework Problem 3.17 Consider the system of three point charges at the right. All charges are positive. The center charge has charge +2Q while the other charges each have charge +Q.

(a)On a separate sheet of paper, draw the field map of the system of charges at the right using 2 lines per Q. Locate the points A and B as carefully as possible on the your field map.

(b)At point A draw the electric field vector based on your

map. Label the vector ~EA.

(c)At point A draw the direction of the force a positive charge would feel if placed at the point. Clearly label this vector ~FA.

(d)At point B draw a barbell dipole with dipole moment pointing to the bottom of the page.

(e)Indicate direction of initial rotation of the dipole.

+Q

+Q

+2Q

A

B

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Homework Problem 3.18 A +2.0nC charge is located at (−1.5m, 0, 0). An −2.0nC charge is located at (+1.5m, 0, 0). The point P is located at (0, 2.6m, 0).

(a)Draw the above system, and draw the individual and resultant electric field vectors at point P .

(b)Find the electric field at point P .

(c)A −10µC charge is placed at point P , find the electric force on this charge.

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Homework Problem 3.19 Three concentric thin spherical shells have charges−Q, +3Q, −Q, and radii a < b < c, respectively. Calculate the electric field everywhere. Draw the electric field everywhere using 4 lines per Q.

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