A super thin and infinitely long rod with uniform charge density, λ = 13.6 nC/m, runs through the center of a half-cylindrical shell with radius, R, and length, L = 1.25 m, as shown in the figure. (a) What is the magnitude of the electric field a perpendicular distance, R, from the infinitely long charged rod? Write a symbolic expression for the magnitude of the electric field, in terms of λ, R, L, and Eo, as needed. E= (b) What is the electric flux through the cylindrical shell? Write a symbolic expression in terms of λ, R, L, and Eo, as needed, then calculate its numeric value. PE = N-m²/C
A super thin and infinitely long rod with uniform charge density, λ = 13.6 nC/m, runs through the center of a half-cylindrical shell with radius, R, and length, L = 1.25 m, as shown in the figure. (a) What is the magnitude of the electric field a perpendicular distance, R, from the infinitely long charged rod? Write a symbolic expression for the magnitude of the electric field, in terms of λ, R, L, and Eo, as needed. E= (b) What is the electric flux through the cylindrical shell? Write a symbolic expression in terms of λ, R, L, and Eo, as needed, then calculate its numeric value. PE = N-m²/C
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Transcribed Image Text:A super thin and infinitely long rod with uniform
charge density, λ = 13.6 nC/m, runs through the
center of a half-cylindrical shell with radius, R, and
length, L = 1.25 m, as shown in the figure.
(a) What is the magnitude of the electric field a perpendicular distance, R, from the infinitely long charged rod?
Write a symbolic expression for the magnitude of the electric field, in terms of λ, R, L, and Eo, as needed.
E =
(b) What is the electric flux through the cylindrical shell? Write a symbolic expression
in terms of λ, R, L, and o, as needed, then calculate its numeric value.
PE
N•m²/C
Expert Solution

Step 1: Know the concept:
Gauss law of electrostatics:
According to this law, the electric flux passing through a closed surface is proportional to the amount of charge stored in its volume. Mathematically,
(1)
where is the electric flux passing through the closed surface,
is the total amount of charge enclosed inside the closed surface, and
is the permittivity of free space.
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