Surface charge density and electric fields in conductors

[ilanwamh]

Physics - Conductors?

Hi, I am currently enrolling Engineering first year and encountered a physics conceptual problem. Please explain to me please, thanks in advance

1. Does conductors have to be in electrostatic equilibrium? if not, how do you calculate the electric field of a non-electrostatic equilibrium conductors?

2. What does it mean by: "On an irregularly shaped conductor, the surface charge density is greatest at locations where the radius of curvature of the surface is smallest"?

Thanks

 

[ranger]

1) Tell us your understanding as it relates to electrostatic equilibrium.

2) The charge they are talking about have the same magnitude. Therefore on a flat surface the charges would repel each other. This repulsion force is directed parallel to the surface. Does that help?

 

[ilanwamh]

To be honest, I have having difficult visualizing conductor, insulator, and conductor electrostatic equilibrium. I know that as for conductor, electrons are freely to move around... But doesn't that disrupt the entire system since electrons are moving and it keeps on attracting protons and repelling proton. I am really confused. A diagram to explain these three would be appreicated.

Thanks

 

[ilanwamh]

The charge they are talking about have the same magnitude. Therefore on a flat surface the charges would repel each other. This repulsion force is directed parallel to the surface. Does that help?

Sorry, I still don't get it, what does it have to do with the density and the radius of curvature of the surface is smallest?

Thanks

 

[ranger]

To be honest, I have having difficult visualizing conductor, insulator, and conductor electrostatic equilibrium. I know that as for conductor, electrons are freely to move around... But doesn't that disrupt the entire system since electrons are moving and it keeps on attracting protons and repelling proton. I am really confused. A diagram to explain these three would be appreicated.

Thanks

Do not think about the localized effects individual charge interactions; they will only confuse you.

When a conductor is in electrostatic equilibrium, the excess charges [on the surface] have positioned themselves in such away as to minimize the repulsive forces. In a state of equilibrium there is no movement of charge on the surface. At this state of equilibrium, the electric field below the surface is zero. At this point the e-field at the surface is perpendicular to the surface.

 

[ranger]

Sorry, I still don't get it, what does it have to do with the density and the radius of curvature of the surface is smallest?

Thanks

Draw a picture with repulsive forces directed along the path connecting the electrons. If you have a straight surface the charges would be evenly spaced. Because of the flat surface the repulsive force is parallel to the surface. Now add some irregularities in the surface (such as bumps); how are electrons affecting each other now?

 

[ilanwamh]

Okay, I guess I won't try and visualize it... because I thought those diagrams in the book would help explain lol, but I guess they don't.

Thanks for helping rangers =)