11/30/2018 HW2
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HW2
Due: 11:59pm on Monday, September 24, 2018
You will receive no credit for items you complete after the assignment is due. Grading Policy
Exercise 22.2
A flat sheet is in the shape of a rectangle with sides of lengths 0.400 and 0.600 . The sheet is immersed in a uniform
electric field of magnitude 60.0 that is directed at 20 from the plane of the sheet .
Part A
Find the magnitude of the electric flux through the sheet.
Express your answer to two significant figures and include the appropriate units.
ANSWER:
Exercise 22.4
It was shown in Example 21.11 (Section 21.5) in the textbook that the electric field due to an infinite line of charge is
perpendicular to the line and has magnitude . Consider an imaginary cylinder with a radius of = 0.130 and a
length of = 0.430 that has an infinite line of positive charge running along its axis. The charge per unit length on the line is
= 7.20 .
Part A
What is the electric flux through the cylinder due to this infinite line of charge?
ANSWER:
Part B
m m
N/C
∘
Φ =
E = λ/2πϵ0 r r m
l m λ
μC/m
Φ = N ⋅ m /C
2
11/30/2018 HW2
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What is the flux through the cylinder if its radius is increased to 0.505 ?
ANSWER:
Part C
What is the flux through the cylinder if its length is increased to 0.810 ?
ANSWER:
Exercise 22.9
A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 18.0 , giving it a charge
of -49.0 .
Part A
Find the electric field just inside the paint layer.
Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of
the sphere and negative value if the field is directed toward the center of the sphere.
ANSWER:
Part B
Find the electric field just outside the paint layer.
Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of
the sphere and negative value if the field is directed toward the center of the sphere.
ANSWER:
Part C
Find the electric field 5.00 outside the surface of the paint layer.
Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of
the sphere and negative value if the field is directed toward the center of the sphere.
ANSWER:
r = m
Φ = N ⋅ m /C
2
l = m
Φ = N ⋅ m /C
2
cm
μC
E =
E =
cm
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Gauss’s Law
Learning Goal:
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 written
where is the permittivity of vacuum.
Part A
How should the integral in Gauss’s law be evaluated?
ANSWER:
Part B Complete previous part(s)
Exercise 22.12
The nuclei of large atoms, such as uranium, with protons, can be modeled as spherically symmetric spheres of charge. The
radius of the uranium nucleus is approximately .
Part A
What is the electric field this nucleus produces just outside its surface?
Express your answer using two significant figures.
ANSWER:
Part B
What magnitude of electric field does it produce at the distance of the electrons, which is about 1.9×10−10
?
Express your answer using two significant figures.
E =
ΦE = ∮ E⋅d = ,
⃗ A⃗ qencl
ϵ0
ϵ0 = 8.85 × 10 /(N ⋅ )
−12 C
2
m2
around the perimeter of a closed loop
over the surface bounded by a closed loop
over a closed surface
92
7.4 × 10
−15 m
E = N/C
m
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ANSWER:
Part 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?
Express your answer using two significant figures.
ANSWER:
A Charged Sphere with a Cavity
An insulating sphere of radius , centered at the origin, has a uniform volume charge density .
Part A
Find the electric field inside the sphere (for
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