Surface charge density of a sphere of radius 10 cm is 8.85*10^-8 C/m^2.Find Potential at the centre of the sphere

Question

experimentx · Answer

hollow sphere or solid sphere??

anonymous · Answer

Solid

experimentx · Answer

potential is constant ... i suppose.

anonymous · Answer

Potential is constant at only the center because E=0 only at the centre

jamesj · Answer

oh wait ... I'm wrong. E = 0 and hence the potential in the interior must be what it is at the surface.

anonymous · Answer

But why?E is only 0 at the centre.Jusr near the centre Enot equal to 0

jamesj · Answer

Yes, it must be because by Gauss's law, the electric flux for any closed surface inside the sphere is zero, because such a surface contains no charge.

experimentx · Answer

first of all ... let's calculate the charge ... total charge

experimentx · Answer

are we supposed to assume that charge is only at surface??

anonymous · Answer

Yes

jamesj · Answer

that is a fundamental result of electricity, that all charge is at the surface.

experimentx · Answer

let me open my old book

anonymous · Answer

All charge is at the surface if and only if it is a conductor.What if it is not

jamesj · Answer

you're told the sphere has 1 value of electric field density, so even if it actually isn't a conductor, it looks like one right now.

jamesj · Answer

**electric CHARGE density.

jamesj · Answer

If you want to brush up on this, watch this juicy lecture: http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-4-electrostatic-potential-and-electric-energy/

anonymous · Answer

Well I suppose that may be true

experimentx · Answer

that would be a great problem in finding the total charge ... but if it were conductor .. our problem will be simplified.

jamesj · Answer

it's easy: $ Q = \sigma A $

anonymous · Answer

Yeah here if it was volume charge density then it would be tough

jamesj · Answer

and you need this.  The electric potential at the surface is
$$ V = \frac{kQ}{r} $$ and that is the potential in the interior as well.

anonymous · Answer

Yeah that's right.I was confused because I was thinking what if it was like charge is spread across the volume of the sphere

experimentx · Answer

yeah i have the same answer

anonymous · Answer

What is the answer?

jamesj · Answer

$$ V = \frac{kA\sigma}{r} $$
now calculate

anonymous · Answer

Yeah Im not getting the correct answer

jamesj · Answer

I guess you could simplify it even one more step to
$$ V = 4 \pi k \sigma r $$