A very long conducting tube (hollow cylinder) has inner radius a and outer radius b . It carries charge per unit length + α , where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length + α . (a) Calculate the electric field in terms of α and the distance r from the axis of the tube for (i) r < a ; (ii) a < r < b ; (iii) r > b . Show your results in a graph of E as a function of r . (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b . It carries charge per unit length + α , where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length + α . (a) Calculate the electric field in terms of α and the distance r from the axis of the tube for (i) r < a ; (ii) a < r < b ; (iii) r > b . Show your results in a graph of E as a function of r . (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +α, where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +α. (a) Calculate the electric field in terms of α and the distance r from the axis of the tube for (i) r < a; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of r. (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?
Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric
field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere.
a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p.
b) Determine the electric field, E(r), for r > R (outside the sphere).
c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere
(r = R)?
d) What is the energy stored in this electric charge configuration?
The charge density of a non-uniformly charged sphere of radius 1.0 m is given as:
For rs 1.0 m; p(r)= Po(1-4r/3)
For r> 1.0 m; p(r)= 0,
where r is in meters.
What is the value of r in meters for which the electric field is maximum?
The volume charge density ρ for a spherical charge distribution of radius R= 6.00 mm is not uniform. (Figure 1) shows ρ as a function of the distance r from the center of the distribution.
a)Calculate the electric field at r = 1.00 mm.
b)Calculate the electric field at r = 1.00 mm.
Chapter 22 Solutions
University Physics with Modern Physics (14th Edition)
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