# Voltage of cylinder of radius R

ε1. The problem statement, all variables and given/known data
A very long solid cylinder of radius R = 6 cm has:
-uniform volume charge density ρ = +7 µC/m3.
-linear charge density λ = 7.9168E-8 C/m

Outside: What is the electric field at a radial distance of 7 cm from the axis of the cylinder?
Inside: What is the electric field at a radial distance of 5 cm from the axis of the cylinder?

Voltage: Setting V=0 at r=3R, find the voltage at the following locations:
V (r = 0)
V (r = R/2)
V (r = R)
V (r = 2R)
V (r = 4R)

2. Relevant equations

using gauss law to find the electric field inside and outside the cylinder

inside the cylinder E = ( ρ*r )/(2*εo)

outside the cylinder E = ( λ )/(2*∏*r*εo)

Voltage is just integration of E, so V=-∫Edr

3. The attempt at a solution

I find the electric field from the axis 0m to 0.07m using E = ( λ )/(2*∏*r*εo), i got 20338.948 N/C

I find the electric field from the axis 0m to 0.05m using E = ( ρ*r )/(2*εo), i got 19773.9484 N/C

The problem i have is to find the voltage from the asked distance to distance r=3R
we set V at 3R = 0.

i do the integration on E = ( ρ*r )/(2*εo) from r=0 to r=R to find the Voltage inside the cylinder

then do integration on E = ( λ )/(2*∏*r*εo) from r=R to r=3R to find the voltage outside the cylinder.

when it ask find the voltage at r=0, it means that i have to find the ΔV, which is from
V(r=0) to v(r=3R), then i do separate integral on that two different E equation, then add them up. Since V at r=3R is 0, then i pretty much ignored it during the integration. but i got it wrong. how am i supposed to do this. i have try many method and i think this is the correctway to do it. can someone help me out or explaining it to me? Thank you for your time and reply

Attached Images
 voltage.jpg (225.8 KB) voltage (2).jpg (216.1 KB)

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