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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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
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,

ϕ equals q subscript n e t end subscript over epsilon subscript 0                                                (1)

where ϕ is the electric flux passing through the closed surface, q subscript n e t end subscript is the total amount of charge enclosed inside the closed surface, and epsilon subscript 0 is the permittivity of free space.


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