Problem 27.21 Part A What is the net electric flux through the cylinder of the f

Question

Problem 27.21

Part A

What is the net electric flux through the cylinder of the figure(Figure 1) ? Assume that Q=250nC and q=8n

An infinite cylindrical rod has a uniform volume charge density (where >0). The cross section of the rod has radius r0. Find the magnitude of the electric field E at a distance r from the axis of the rod. Assume that r<r0.

Part C

Find the magnitude E of the electric field at a distance r from the axis of the cylinder for r<r0.

Keep in mind that we've chosen the label l to represent the length of the cylindrical Gaussian surface.

Express your answer in terms of some or all of quantities , r, r0, l, and 0.

Please look at the quetions that I posted 20 mins ago all of them were incorrect please review the last 4 questions too please and thank you

Explanation / Answer

part A:

as per gauss' law,

total electric flux crossing through a surface is given by charge enclosed/electrical permitivity

here charge enclosed=q=8 nC=8*10^(-9) C

then electric flux=8*10^(-9)/(8.85*10^(-12))=903.95 N.m^2/C

part C:

consider a concentric cylidrical surface of the same length L and of radius r.

then charge enclosed=pho*pi*r^2*L

using gauss' law:

if electric field is E,

then epsilon*E*2*pi*r*L=pho*pi*r^2*L

==>E=pho*r/(2*epsilon)

hence electric field magnitude at a distance of r when r<r0 is given by pho*r/(2*epsilon)

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