full points to anyone who answers in detail all of the questions An infinitely l

Question

full points to anyone who answers in detail all of the questions

An infinitely long cylindrical tube with a cross section shown below has a volume charge density of 10.0 mu C/m3. The outer radius is 10.0 cm, and the radius of the hollow region is 5.0cm. Point A is at the center of the cylinder. Find the electric field everywhere inside the hollow region. Find the electric potential difference between points A and B. At which point is the potential greater? Sketch the electric field and potential lines inside the hollow region.

Explanation / Answer

a)

consider a solid cylinder with no hollow part in it -->C1

and consider a solid cylinder which fits perfectly to the hollow part--->C2

E1 from C1 is

by guass law

E1 = q1/(e*2pi r1*l)

where e is epselon

r1 is the radial distance from A

l is the length of the guassian cylinder considered

q1= 10.0 * pi*r1*r1*l*10^(-6)

E1=10^(-5)*r1/2e in radially outward direction w.r.t center A

let the center point between A and B is C

then we have for Cylinder C2

E2 = q2/(e*2pi*r2*l)

where

r2 is the radial distance from C

l is the length of the guassian cylinder considered

q2= 10.0 * pi*r2*r2*l*10^(-6)

E2=10^(-5)*r2/2e in radially outward direction w.r.t center C

so the actual electric field is

E1-E2= 10^(-5)*(r1+r2) / 2e from A to C as radially outward is in opposite direction

E1 - E2 = 10^(-5)*(r1-r2) / 2e from C to B as radially outward is in same direction

b) for point A r1=0 and r2=2.5

for point B r1=5 and r2=2.5

so EA= 10^(-5)*2.5/(2e)

EB= 10^(-5)*2.5/(2e)

along the straight line AB

from A to C

we have

potential difference = 10^(-5)*2.5*2.5/4e

form C to B

we have

potential difference = 10^(-5)*2.5*2.5/4e

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