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Homework Statement
I'm reading GriffithIntroduction to electrodynamics, In chapter 2 about electrostatics, I've encounter few problems that I've managed, to solve (luck !!), I'm asked to calculate the electric field due to a charged disk of radius R in a point P above the center (Pic)
Homework Equations
Electric field due to uniform continuous charge distrubition
[tex] \vec E = \frac {1}{4 \pi \epsilon _0} \int \int \frac {\sigma \hat{r}}{r^2}dS[/tex]
The Attempt at a Solution
I've tried to use the usual approach, that is cutting the disk into little circles, [itex] \lambda = \frac {Q}{L} = \frac{\sigma A }{L} = \frac{\sigma 2 \pi r dr}{2 \pi r} = \sigma \cdot dr [/itex]
The electric field due to that circle is [itex] \vec E_z = \frac {\lambda}{4\pi\epsilon_0} \int \frac{dArc}{(R^2 + z^2)^\frac{3}{2}} = \frac {\lambda}{4\pi\epsilon_0} \int_0^{2\pi}\frac {zR \cdot d\theta}{(R^2 + z^2)^\frac{3}{2}} [/itex],You just multiply by 2 [itex]\pi[/itex] and sub the [itex]\lambda[/itex] , [itex] \vec E_z = \frac{\sigma zR \cdot dr}{2\pi\epsilon_0}\frac{1}{(R^2 + z^2)^\frac{3}{2}} [/itex], I should have written[itex] d\vec E_z [/itex] because we'll integrate that from 0 up to R, so [tex] \vec E_z = \frac{\sigma}{2\pi\epsilon_0(R^2 + z^2)^\frac{3}{2}} \int_0^zR\cdot dr = \frac{\sigma zR^2}{2\pi\epsilon_0(R^2 + z^2)^\frac{3}{2}}[/tex], I know that this is wrong, so can someone tell me where I've messed things up ?
One more Request, where can I find more problems about electrostatics, I need some practice Thanks !!
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