PHYS112 WVU Field Maps and Gauss’s law The questions in this section are to be answered by circling the correct multiple-choice answer AND providing a shor

PHYS112 WVU Field Maps and Gauss’s law The questions in this section are to be answered by circling the correct multiple-choice answer AND
providing a short justification of your answer in the space after the problem.. Name:
Lab Day/Time:
Wednesday Homework 3 Field Maps and Gauss’ Law
Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiplechoice 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.
Multiple Choice Problems
The questions in this section are to be answered by circling the correct multiple-choice answer AND
providing a short justification of your answer in the space after the problem..
Wednesday Homework Problem 3.1 Two parallel infinite planes
of charge (shown in the figure) have charge densities 34 σ and −2σ.
Compute the field in the outermost regions, I and III.
3
σ
4
I
II
x
Select One of the Following:
~ I = +5σ/4ε0 x̂ , E
~ III = −5σ/4ε0 x̂
(a) E
~ I = −3σ/8ε0 x̂ , E
~ III = −σ/ε0 x̂
(b) E
~ I = −σ/2ε0 x̂ , E
~ III = +σ/2ε0 x̂
(c) E
~ I = +5σ/8ε0 x̂ , E
~ III = −5σ/8ε0 x̂
(d) E
~ I = +σ/2ε0 x̂ , E
~ III = −σ/2ε0 x̂
(e) E
1
-2σ
III
Wednesday Homework Problem 3.2 Two infinite parallel planes
of charge with uniform surface charge densities are parallel to the
y − z plane and equally spaced about the origin. The planes pass
through the points ±5cm. The plane passing through +5cmx̂ has
surface charge density +3σ. The plane passing through −5cmx̂
has surface charge density −5σ. The planes are drawn to the
right. Compute the electric field at the origin.
-5 σ
y
3σ
Select One of the Following:
x
(a) + 2ǫσ0 x̂
(b) − 4σ
ǫ0 x̂
(c) + 4σ
ǫ0 x̂
(d) − ǫσ0 x̂
4σ
(e) − 4ǫ
x̂
0
4σ
(f) + 4ǫ
x̂
0
Wednesday Homework Problem 3.3 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 the electric field in Region
II between the two shells (a < r < b). y III II Select One of the Following: a I Air (a) 0 σ r̂ 4πε0 r2 σ + r̂ 4πε0 r2 4πa2 σ − r̂ 4πε0 r2 4πa2 σ + r̂ 4πε0 r2 −4πa2 σ + 8πb2 σ r̂ 4πε0 r2 (b) − (c) (d) (e) (f) Air Air 2 x b Wednesday Homework Problem 3.4 Two infinite planes of charge are drawn to the right. One infinite uniform plane of charge occupies the x − y plane with charge density, σxy = 2.0µC/m2 . Another infinite uniform plane of charge occupies the y − z plane with charge density, σyz = 3.0µC/m2 . Compute the electric field at ~rP = (−3.0cm, 0, 3.0cm). z + P + + Select One of the Following: (a) 6.0 × 104 N C x̂ (b) −2.8 × (c) −1.7 × (d) −1.0 × (e) −1.1 × (f) −3.4 × 105 N C ẑ 105 N C x̂ 3N 10 C x̂ 105 N C x̂ 105 N C x̂ + + 1.1 × 105 N C ẑ + 3.1 × 103 N C ẑ + + + + + + + + + + + x + 1.7 × 105 N C ẑ + 2.2 × 105 N C ẑ Wednesday Homework Problem 3.5 A pith ball with charge +1.5nC is fixed at the origin. A second +1.5nC pith ball floats vertically above the first. Modelling both pith balls as point charges, compute the center-to-center separation of the two pith balls. The mass of a pith ball is 6.0 × 10−5 kg. Note, the distance calculated may or may not be larger than the radius of the pith ball. Select One of the Following: (a) 5.9 × 10−3 m (b) 3.4 × 10−5 m (c) 6.3 × 10−1 m (d) 1.3m (e) 150m 3 Open Response Questions Wednesday Homework Problem 3.6 Six positive charges Q are arranged in a circular pattern as shown to the right. C (a)Compare the strength of the electric field at points A and B. Is the field stronger, weaker, or about the same at these locations? (b)On a full sheet of paper, draw the field map using 2 lines per Q. +Q (c)Draw the direction of the acceleration of an electron placed at point B. (d)Draw a dipole (two charges on a stick) at point C with dipole moment pointing to the left of the page. (e)Draw the direction of rotation of the dipole in (d). 4 +Q +Q A +Q B +Q +Q Wednesday Homework Problem 3.7 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. 5 Wednesday Homework Problem 3.8 A point charge with charge −Q is concentric with two thin charged shells. The inner shell has total charge +2Q and the outer shell has total charge −3Q. Draw the field everywhere using 4 lines per Q. Compute the field everywhere. Clearly show the Qenc used in each region. III −3Q II +2Q I −Q Air Air Air 6 Wednesday Homework Problem 3.9 A uniform volume charge occupies the region r < a and has volume charge density ρ. The total charge of the volume charge is +2Q. A thin spherical shell of radius b > a surrounds the volume charge. The total charge of
the thin spherical shell is −Q.
shell charge
Air
b
(a)Draw the electric field map with 4 lines per Q.
Air
(b)Calculate the electric field everywhere.
volume a
charge
I
II
III
7

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