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