A uniform volume charge occupies the region r < a and has volume charge density ρ....
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 −2Q.
(a)Draw the electric field map with 4 lines per Q on the
figure to the right.
(b)Calculate the electric field everywhere. This part is to
be
worked symbolically (no decimal numbers should be in
your solution).
(c)Suppose a = 15cm, b = 25cm, ρ = 3.0 × 10−8C/m3,
and Q = 2.1 × 10−10C, compute the field ~EP at ~rP =
(10cm, 10cm, 0).
I
II
III
Please answer carefully. I am stuck on part C).
Homework Answers
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A uniform volume charge
occupies the region r < a and has volume charge density ρ....
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 ,...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 , where A is a constant and r is measured from the center of the sphere. a) Show that the electric field outside the sphere (r > R) is E = AR5 /(5εor 2 ). b) Show that the electric field inside the sphere (r < R) is E = AR3 /(5εo). Hint: The total charge Q on the sphere is found by integrating ρ...
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A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0.), where r is the radius from the center of the sphere, a is constant, and a > 0. magnitude E= (b)...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R. Hint: Let dV be a spherical shell of radius r and thickness dr. What...
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ...
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A solid sphere of nonconducting material has a uniform positive charge density ρ (i.e. positive charge...
A solid sphere of nonconducting material has a uniform positive charge density ρ (i.e. positive charge is spread evenly throughout the volume of the sphere; ρ=Q/Volume). A spherical region in the center of the solid sphere is hollowed out and a smaller hollow sphere with a total positive charge Q (located on its surface) is inserted. The radius of the small hollow sphere R1, the inner radius of the solid sphere is R2, and the outer radius of the solid...
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6. An infinite cylinder of radius R has a uniform charge density of ρ in its interior, and a surface charge side and outside the cylinder. Be density of -pR on its surface. Find the electric field everywhere in clear about both the magnitude and direction of the field.
A thick, spherical, insulating shell has an inner radius a and an outer radius b. The region a< r < b has a volume charge density given by p = A/r where A is a positive constant.
PROBLEM 2: A thick, spherical, insulating shell has an inner radius a and an outer radius b. The region a< r < b has a volume charge density given by p = A/r where A is a positive constant. At the center of the shell is a point charge of electric charge +q Determine the value of A such that the electric field magnitude, in the region a < r < b, is constant.
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ...
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ 2.14 nC/m , inner radius a-12.8 cm, and outer radius b = 2.6a. what is the magnitude of the electric field at rad distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b? Units (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number Units Units...
Charge is distributed throughout a spherical volume of radius R with a density ρ ar where...
Charge is distributed throughout a spherical volume of radius R with a density ρ ar where α is a constant. an risthe distance from the center of the sphere. Determine the electric field due to the charge at a point a distance r from the center that is inside the sphere, and at a point a distance r from the center that is outside the sphere. (Enter the radial component of the electric field. Use the following as necessary: R,...
Figure 23-51 shows a spherical shell with uniform volume charge density ρ = 1.76 nC/m3, inner...
Figure 23-51 shows a spherical shell with uniform volume charge
density ρ = 1.76 nC/m3, inner radius a
= 11.0 cm, and outer radius b = 2.10a.
What is the magnitude of the electric field at the following
radial distances:
(a) r = 0:
0 N/C
(b) r = a/2.00:
0 N/C
(c) r = a:
0 N/C
(d) r = 1.50a:
______ N/C
(e) r = b:
______ N/C
(f) r = 3.00b:
_______N/C
Figure 23-51
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ = 2.01 nC/m3, inner radius a = 9.50 cm, and outer radius b = 3.4a, what is the magnitude of the electric field at radial distances (a) r = 0; (b) r-a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r-3.00b?
6. An infinite cylinder of radius R has a uniform charge density of ρ in its interior, and a surface charge side and outside the cylinder. Be density of -pR on its surface. Find the electric field everywhere in clear about both the magnitude and direction of the field.
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ 2.14 nC/m , inner radius a-12.8 cm, and outer radius b = 2.6a. what is the magnitude of the electric field at rad distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b? Units (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number Units Units...
Charge is distributed throughout a spherical volume of radius R with a density ρ ar where α is a constant. an risthe distance from the center of the sphere. Determine the electric field due to the charge at a point a distance r from the center that is inside the sphere, and at a point a distance r from the center that is outside the sphere. (Enter the radial component of the electric field. Use the following as necessary: R,...
Figure 23-51 shows a spherical shell with uniform volume charge
density ρ = 1.76 nC/m3, inner radius a
= 11.0 cm, and outer radius b = 2.10a.
What is the magnitude of the electric field at the following
radial distances:
(a) r = 0:
0 N/C
(b) r = a/2.00:
0 N/C
(c) r = a:
0 N/C
(d) r = 1.50a:
______ N/C
(e) r = b:
______ N/C
(f) r = 3.00b:
_______N/C
Figure 23-51
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