An infinitely long rod lies along the x-axis and carries a uniform linear charge density λ = 5 μC/m. A hollow cone segment of height H = 27 cm lies concentric with the x-axis. The end around the origin has a radius R1 = 8 cm and the far end has a radius R2 = 16 cm. Refer to the figure. a. Consider the conic surface to be sliced vertically into an infinite number of rings, each of radius r and infinitesimal thickness dx. Enter an expression for the electric flux differential through one of these infinitesimal rings in terms of λ, x, and the Coulomb constant k. b. Integrate the electric flux over the length of the cone to find an expression for the total flux through the curved part of the cone (not including the top and bottom) in terms of λ, H, and the Coulomb constant k. Enter the expression you find. c. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = 0. d. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = H. e. Enter an expression for the total electric flux through the entire surface of the cone in terms of defined quantities. f. Enter an expression for the total electric flux through the cone in terms of the net charge Qenc contained inside the cone. Note that the total flux does not depend on the size of the cone, but on the amount of charge enclosed in it. g. Calculate the total flux through the surface of the cone in units of kN•m2/C
An infinitely long rod lies along the x-axis and carries a uniform linear charge density λ = 5 μC/m. A hollow cone segment of height H = 27 cm lies concentric with the x-axis. The end around the origin has a radius R1 = 8 cm and the far end has a radius R2 = 16 cm. Refer to the figure.
a. Consider the conic surface to be sliced vertically into an infinite number of rings, each of radius r and infinitesimal thickness dx. Enter an expression for the electric flux differential through one of these infinitesimal rings in terms of λ, x, and the Coulomb constant k.
b. Integrate the electric flux over the length of the cone to find an expression for the total flux through the curved part of the cone (not including the top and bottom) in terms of λ, H, and the Coulomb constant k. Enter the expression you find.
c. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = 0.
d. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = H.
e. Enter an expression for the total electric flux through the entire surface of the cone in terms of defined quantities.
f. Enter an expression for the total electric flux through the cone in terms of the net charge Qenc contained inside the cone. Note that the total flux does not depend on the size of the cone, but on the amount of charge enclosed in it.
g. Calculate the total flux through the surface of the cone in units of kN•m2/C
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