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?
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area.
What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2?
Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.
Charge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E is measured along the ring’s central axis (perpendicular to the plane of the ring). At what distance from the ring’s center is E maximum?
In the figure a sphere, of radius a = 13.2 cm and charge q = 6.00×10-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 37.0 cm and outer radius c = 39.0 cm . This shell has a net charge of -q. Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r< a). Evaluate for r=6.6 cm. Find expressions for the electric field as a function of the radius r, between the sphere and the shell (a< r <b). Evaluate for r=25.1 cm. Find expressions for the electric field as a function of the radius r, inside the shell (b< r <c). Evaluate for r=38.0 cm
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