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...
6. An infinite cylinder of radius R has a uniform charge density of ρ in its...
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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