- #1
kesaluj
Homework Statement
In a lab experiment we measured the potential at different points within a cylindrical capacitor electric field modeling plate thing (apparently that's the best I could do to translate that into English). The positive electrode was connected in the middle and the negative one was on the outside. The measured values decreased as we got further away from the center.
Homework Equations
3. The Attempt at a Solution [/B]
The part I'm unsure about (other than what to even call this experiment) is the theoretical values. We were given these two formulas:
[tex]V(r) = \frac {U \cdot \ln(\frac {r}{r_o}) }{\ln(\frac {r_o}{r_i})},[/tex]
[tex]E(r) = - \frac {U }{r \cdot \ln(\frac {r_o}{r_i})},[/tex]
where [itex]r_o[/itex] is the outer radius, [itex]r_i[/itex] is the inner radius, and [itex]U[/itex] is the voltage used. Both of them result in negative values, since [itex]r_o[/itex] is clearly larger than [itex]r[/itex] in the logarithm in first equation and there's a minus sign in the second one. The absolute values, though, look about right.
I've tried to research this, but my mediocre physics knowledge is failing me. I get that this is a Gaussian surface thing and I know that we're looking at the [itex]\frac {V_{{r_o-}{r}}} {V_{r_i-r_o}}[/itex] proportion, but I'm having a hard time making sense of the negative values, especially since we were straight-up given these formulas in the lab report instructions.
Does anyone have any pointers?