# Voltage of cylinder of radius R

**1. 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

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