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

In summary, the experts in the conversation are discussing the surface charge density of a conductor and whether it is evenly distributed or not. They mention that in an ideal conductor, the potential is uniform and there are no potential differences on the surface. However, this may not be the case for a non-spherical conductor. The experts also point out that surface charge density is inversely related to the radius of the conductor.
  • #1
baby_1
159
15
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 ?
3065864600_1403087286.jpg

if isn't why and how the surface charge density spread?
Thanks
 
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  • #2
What are your thoughts? Compare the given shape to, say, a sphere. What is the difference?
 
  • #3
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?
7272210400_1403158339.jpg

if yes? why surface charge density should be same?
if no?how can find surface charge density at different point and different shape?
 
  • #4
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...
 
  • #5
BvU said:
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 [itex]\displaystyle V(R)=\frac{Q}{4\pi\epsilon_0 R}= \frac{\sigma R}{\epsilon_0}[/itex]

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

attachment.php?attachmentid=70728&stc=1&d=1403238050.jpg


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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  • #6
BvU said:
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.
 
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  • #7
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 ?
 
  • #8
BvU said:
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).
 

1. What is charge density on the surface of a conductor?

Charge density on the surface of a conductor refers to the amount of electric charge per unit area on the surface of the conductor. It is a measure of how densely packed the electric charges are on the surface of the conductor.

2. How is charge density on the surface of a conductor measured?

Charge density on the surface of a conductor can be measured using an instrument called an electrostatic voltmeter. This instrument measures the potential difference between the surface of the conductor and a reference point, which can then be used to calculate the charge density.

3. Why is charge density on the surface of a conductor important?

Charge density on the surface of a conductor is important because it determines the strength of the electric field on the surface of the conductor. This, in turn, affects the behavior of the charges on the surface and the distribution of charges within the conductor.

4. How does the charge density on the surface of a conductor affect its conductivity?

The charge density on the surface of a conductor can affect its conductivity by influencing the movement of charges within the conductor. A higher charge density can result in a stronger electric field, which can hinder the movement of charges and decrease conductivity.

5. Can the charge density on the surface of a conductor be controlled?

Yes, the charge density on the surface of a conductor can be controlled by manipulating the amount and distribution of charges on the surface. This can be done through methods such as applying an external electric field or changing the surface material of the conductor.

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