## anonymous 4 years ago Electric potential. I have posted the questions as a picture. I hope somebody can help me.

1. anonymous

2. anonymous

Could you write down Gauss' Law?

3. nikvist

Electric field for r>a $E\sim\frac{1}{r^2}$

4. anonymous

Electric field shall be calculated at all points in the space Calculate charge enclosed by sphere of radius r $Q=\int\limits_{0}^{r}p(r)4\pi r^2dr$ we find $Q'=\frac{Q}{a}r$ nor apply guass's law for spherical symmetry $E=\frac{Qr}{4\pi r^2a \epsilon_0}$ now do this $V=-\int\limits_{r}^{\infty}Edr$

5. anonymous

There are a few changes You must see through the now

6. anonymous

Feel'in lazy to type

7. anonymous

Above relation for E is for 0<r<a for r>a $E=\frac{Q}{4\pi \epsilon_0r^2}$

8. anonymous

Now potential $Q=-\frac{Q}{4\pi \epsilon_0r}$ for r>a 0<r<a $V(r)=-\frac{Q}{4\pi \epsilon_oa}+\frac{Q}{4\pi a \epsilon_o}\ln(\frac{a}{r})$