# So basic question about Charge density on the surface of the conductor

#### baby_1

Hello
I want to know surface charge density of the conductor in all part of that is same or not?
for example in this shape ?

if isn't why and how the surface charge density spread?
Thanks

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#### CAF123

Gold Member
What are your thoughts? Compare the given shape to, say, a sphere. What is the difference?

#### baby_1

Thanks dear CAF123
you mean surface charge density at different point of a conductor are the same? point 1 and 2 have same surface charge density?

if yes? why surface charge density should be same?
if no?how can find surface charge density at different point and different shape?

#### BvU

Homework Helper
Dear baby,

Just for my information: is there an external electric field ?

A (ideal) conductor is characterized by the fact that there are no potential differences between points on the surface. If there were, the charge would move until there are no more.

In the absence of an external field that means all electric field lines are perpendicular to the surface and equipotential lines parallel to it. Hence evenly distributed surface charge...

#### SammyS

Staff Emeritus
Homework Helper
Gold Member
Dear baby,

Just for my information: is there an external electric field ?

A (ideal) conductor is characterized by the fact that there are no potential differences between points on the surface. If there were, the charge would move until there are no more.

In the absence of an external field that means all electric field lines are perpendicular to the surface and equipotential lines parallel to it. Hence evenly distributed surface charge...
Actually, it has a unevenly distributed surface charge.

For an isolated conducting sphere, the potential at the surface is given by $\displaystyle V(R)=\frac{Q}{4\pi\epsilon_0 R}= \frac{\sigma R}{\epsilon_0}$

Consider each end of the conductor you show in the figure.

The left end appears to be a section of a sphere with a relatively large radius. The right end a section of a sphere with much smaller radius.

It's clear that the surface charge density, σ, depends upon the radius of curvature.

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#### sankalpmittal

Dear baby,

Just for my information: is there an external electric field ?

A (ideal) conductor is characterized by the fact that there are no potential differences between points on the surface. If there were, the charge would move until there are no more.

In the absence of an external field that means all electric field lines are perpendicular to the surface and equipotential lines parallel to it. Hence evenly distributed surface charge...
I disagree. See SammyS' post.

Surface charge density is governed by equation :

σ1r12r2

when you connect two conductors. From here surface charge density is inversely related to the radius of conductor.

So at peaks charge density is maximum and it's unevenly distributed.

#### BvU

Homework Helper
I stand corrected for my last sentence! My "Hence evenly distributed surface charge... " wasn't thought through. Too many simple spherically symmetric exercises...

I hope the stuff before can stay standing, though ?

#### SammyS

Staff Emeritus
Homework Helper
Gold Member
I stand corrected for my last sentence! My "Hence evenly distributed surface charge... " wasn't thought through. Too many simple spherically symmetric exercises...

I hope the stuff before can stay standing, though ?
Yup.

The potential is uniform throughout the conductor (under electrostatic conditions).

"So basic question about Charge density on the surface of the conductor"

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