- #1

Mr.Tibbs

- 24

- 0

Equations:

C=[itex]\frac{εS}{r}[/itex] ; S-area of the plates; r-distance

i(t)=C[itex]\frac{dv}{dt}[/itex]

Approach:

for starters I subbed the capacitance equation into the current equation and achieved this result:

i(t)=[itex]\frac{εS}{r}[/itex]*[itex]\frac{dv}{dt}[/itex]

taking the first derivative of the voltage and subbing it into the equation gives me:

i(t)=[itex]\frac{εS}{r}[/itex]*-V[itex]_{0}[/itex]ωsin(ωt)

Now I divide both sides of the equation by S in order to get the current density. I then integrate this equation with respect to r from the inner radius to the outer radius:

J[itex]_{d}[/itex](t)=-[itex]\frac{εV_{0}sin(ωt)}{ln(b/a)}[/itex]

More or less I don't know if I computed this correctly so any help would be appreciated.