Why is this 0? Help Gauss's law

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Homework Help Overview

The discussion revolves around the application of Gauss's law to determine the electric field around a long straight metal rod with a specified charge per unit length. Participants are exploring the implications of the rod being a conductor versus an insulator.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the electric field inside conductors and question why the electric field is zero within the metal rod. There is an exploration of the differences between conducting and insulating materials, particularly regarding charge distribution.

Discussion Status

Several participants have provided insights into the nature of electric fields in conductors versus insulators. There is an ongoing examination of the assumptions related to the charge distribution and the applicability of certain equations to different types of materials. No explicit consensus has been reached, but productive lines of questioning are evident.

Contextual Notes

Participants are considering the implications of the problem setup, particularly the distinction between a metal rod and an insulating rod, which affects the electric field calculations. The discussion includes references to specific equations and their relevance to different scenarios.

flyingpig
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Homework Statement



A long straight metal rod has a radius of 5.00cm and a charge per unit length of 30.0nC/m. Find the electric field

a) 3.00cm

The Attempt at a Solution



It says a) = 0

I did some math and I got

2k\frac{\lambda}{r}

The rod is solid, so should a E-field be radially outward from its symmetrical axis?
 
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I am assuming that, what you wrote as, "the electric field a) 3.00cm" means "the electric field at 3.00cm from the center of the wire"


Answer to this question first: If you have a conducting sphere, carrying a charge say Q, than what is the electric field at a point inside it??
 
first check theory on electric field inside conductors.
 
Mandeep Deka said:
I am assuming that, what you wrote as, "the electric field a) 3.00cm" means "the electric field at 3.00cm from the center of the wire"


Answer to this question first: If you have a conducting sphere, carrying a charge say Q, than what is the electric field at a point inside it??

k\frac{q}{a^3}r for a < r
 
it is a metal rod. so all the charge would reside on the surface only, none can stay in the bulk.

so the field inside the rod is zero.
 
flyingpig said:
k\frac{q}{a^3}r for a < r

its for symmetrical charge distribution throughout volume. metals can't have that, all of their charge resides on surface! Can you tell why?

and i believe it must be "r<a"
 
graphene said:
it is a metal rod. so all the charge would reside on the surface only, none can stay in the bulk.

so the field inside the rod is zero.

So, but a metal sphere can too? Isn't that what my equation is?

Oh wait, I think I get it. The key here is that my equation is for an insulating sphere, not a conducting one. Hence.
 
flyingpig said:
So, but a metal sphere can too? Isn't that what my equation is?

Oh wait, I think I get it. The key here is that my equation is for an insulating sphere, not a conducting one. Hence.

Yes now you're right
 
cupid.callin said:
Yes now you're right

If this was not a "metal" rod, or "insulating rod", then my numbers in the above would be right, right?
 
  • #10
i can't get you
 
  • #11
cupid.callin said:
i can't get you

If it is insulating, all the charges would be stuck and won't be all on the surface
 
  • #12
flyingpig said:
k\frac{q}{a^3}r for a < r

If you are saying that this formula is for insulating sphere then you are right!

And also for the explanation, the charges will not move to the surface!

can you find the same for insulating cylinder?
 
  • #13
flyingpig said:
k\frac{q}{a^3}r for r<a

If you are saying that this formula is for insulating sphere then you are right!

And also for the explanation, the charges will not move to the surface!

can you find the same for insulating cylinder?
just draw a gaussian surface with r < radius of cylinder and coaxial with cylinder and use gauss theorem
 

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