Several Questions on Electric Potential

[Divergent13]

Hey everyone, I just wanted to ask these two questions on electric potential that are having me a bit stuck:

A thin rod of length 2L is centered on the x-axis on a coordinate plane... The rod carries a unif. distr. charge Q. Determine the potential V as a funct of y for the points along the Y axis.

My problem with this--- its not an infinite rod! I understand that since this rod is of specified length, we will have to some tricky math here and end up doing an integral with our limits for the rod (IE -L and L)... but would all this be is essentially the equation one can derive for the same situation for ELECTRIC FIELD, and just multiply by r? (Where r is the dist on the y axis)



Another Question is suppose a conducting sphere of diameter d is charged to a certain voltage V relative to V = 0 at r = infinity.

How can we find an equation sets up the surface charge density sigma?
(Just in general)


I appreciate any help thanks.

 

[eJavier]

Electric Field:

$$\def\vr{\mathord{\vec r}} \providecommand{\abs}[1]{\lvert #1 \rvert}<br /> \vec E (\vr) = \frac{1}{4 \pi \epsilon_0}\int\frac{\rho(\vr\ ')(\vr-\vr\ ')}{\abs{\vr-\vr\ '}^3}d l'$$

Electric potential:
$$\def\vr{\mathord{\vec r}} \providecommand{\abs}[1]{\lvert #1 \rvert}<br /> &\phi(\vr)=\frac{1}{4\pi\epsilon_0}\int \frac{\rho(\vr\ ')}{\abs{\vr-\vr\ '}}d l '$$

And for the 2nd prob

$$E_{outside shell} - E_{inside shell} = \frac {\sigma}{\epsilon_0} \vec n$$

Where n is the unit normal vector pointing out of the shell

 

[Divergent13]

Excellent that first one makes perfect sense now--- thank you.