Electric Field of an Infinite Line of Charge: Analyzing the Rod

In summary, the shell has no electric field and so does not contribute to the electric field inside the shell. The formula for the length charge density is λ = Q/L, where Q is the charge over a length and L is the surface area of the shell.
  • #1
vorcil
398
0
http://img197.imageshack.us/img197/2942/assgn3q1.jpg [Broken]

I took a good crack at this question, could somebody please check?

a)
I thought the shell could be modeled as a conductor with a hole in it,
as there is no electric flux inside a hole of a conductor and the charge of the shell is on the outside of the surface, there is no electric field, so the shell does not contribute to the electric field inside the shell

- this leaves the infinitely long rod!
I'm assuming the rod can be modeled as an infinite line of charge
and the formula for the electric field it creates is

(1/(4pi(epislon nought) ) ) * (2 lavender)/r
-n.b i would go through the proof of this formula but it's so long! and we all know it lol.

- the 2 cancels out 2pi
so the end formula is

lavender / 2pi * episolon nought * r

please check





b) the inner surface charge density? LOL Inner and surface made me automatically think the surface charge density of the inside of the rod is 0

but i know you'll probably want my proof
i know that it is a conducting rod, so all the charges get sent to the surface of the rod and there is no electric field/and flux inside SO my awnser is 0?
(can someone tell me why the charges get sent to the 0? I thought that it would be uniformly charged in a conductor, but at electrostatic equillibrium)









c)(will postsoon, i just need some time to do them)
 
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  • #2


vorcil said:
b) the inner surface charge density? LOL Inner and surface made me automatically think the surface charge density of the inside of the rod is 0

but i know you'll probably want my proof
i know that it is a conducting rod, so all the charges get sent to the surface of the rod and there is no electric field/and flux inside SO my awnser is 0?
(can someone tell me why the charges get sent to the 0? I thought that it would be uniformly charged in a conductor, but at electrostatic equillibrium)

I got it wrong, It is non-zero apparently?

this is mastering physic's response:

mastering physics said:
FeedbackRemember that the electric field inside a conductor must be zero. Thus, your gaussian surface must inclose a total charge of zero. However, we know that the rod has some finite charge, and thus the charge density on the inner surface must be none-zero.
 
  • #3


c)
I know the charge on the shell is -2λ
the formula for length charge density is λ = Q/L
that means, Q(the charge over a length) = -2λ * L

we want the surface charge density so I'm lookin for Q/A

the the surface area of a rod = pi*r² * L

we want q/a,
(-2λ * L) / pi*r² * L
leaving me with
-2λ / pi*r²
 
  • #4


still lookin for help with B) please
 
  • #5


vorcil said:
c)
I know the charge on the shell is -2λ
the formula for length charge density is λ = Q/L
that means, Q(the charge over a length) = -2λ * L

we want the surface charge density so I'm lookin for Q/A

the the surface area of a rod = pi*r² * L

we want q/a,
(-2λ * L) / pi*r² * L
leaving me with
-2λ / pi*r²

HOW DID I GET THIS WRONG?
mastering physics is bloody stupid
 
  • #6


I got it wrong, It is non-zero apparently?

They are asking what the surface charge density is on the inner surface of the shell, NOT the rod. In fact the rod doesn't even have an inner surface.
 
  • #7


Cyosis said:
They are asking what the surface charge density is on the inner surface of the shell, NOT the rod. In fact the rod doesn't even have an inner surface.

so it's the same as the charge on the outside of the shell?

- is C) right?
 
  • #8


I think i may have gone wrong for finding the surface charge density on the outside of the shell

it's 2*pi*r * L

so
Q / 2pi*r * L is what I'm looking for

-

Q = λ*L

-2λ*L = Q

-2λ / 2*pi*r = answer?
 
  • #9


You're correct that you calculated the area of the shell incorrectly. However how does the calculation you're attempting now differentiate between the inner surface and the outer surface? Can you provide any arguments why exactly this pertains to the outer surface?
 
  • #10


Cyosis said:
You're correct that you calculated the area of the shell incorrectly. However how does the calculation you're attempting now differentiate between the inner surface and the outer surface? Can you provide any arguments why exactly this pertains to the outer surface?

I can't provide any arguments,

I know the surface charge density on the inside of the shell is exactly the same as the surface charge density on the outside

i don't know how to differentiate between the field created outside the shell and inside the shell,

except that i know the field inside the shell should cancel out because of it being orientated in a circle

-
any other tips please?
 
  • #11


Since the shell is a conductor the electric field inside the shell is indeed zero, as hinted by MP.

What are your arguments for thinking that the surface charge density is the same on both the inner an outer surface?
 
  • #12


well it's a conducting shell

and also it dosen't state a thickness, only a length and radius from centre of the shell
 
  • #13


well it's a conducting shell

This is not an argument. If the conducting shell would have had no charge on it what would the surface charge density be?
 
  • #14


Cyosis said:
This is not an argument. If the conducting shell would have had no charge on it what would the surface charge density be?

zero,

I ment that the cylindrical shell is made of a material that allows charge to be conducted through it?
 
  • #15


It would not be zero. Could you explain to me what a conductor is?
 
  • #16


Cyosis said:
It would not be zero. Could you explain to me what a conductor is?

something/a medium that allows electrons to flow freely?
things like metals are conductors
things like rubber are insulators

i know conductors allow electrons to flow freely because they have valence shell electrons (or the outer atoms aren't held in very well)
 
  • #17


Cyosis said:
It would not be zero. Could you explain to me what a conductor is?

i see what you mean, i should've said electrons instead of charge
because positive charges (from protons) aren't able to flow through a conductor, but charge from electrons are (what about positrons?)
 
  • #18


More precisely something that allows charges to flow freely. So if the conductor in your problem would have a zero line charge density, would you still think that the surface charge density would be zero as well? Explain your answer.

Hint: What happens to the charges if you put a conductor in an electric field.
 

What is an infinite line of charge?

An infinite line of charge is a hypothetical concept in physics where a line of charge extends infinitely in both directions without any interruptions or end points. It is used to simplify calculations and understand the behavior of electric fields.

How is the electric field of an infinite line of charge calculated?

The electric field of an infinite line of charge is calculated using the formula E = λ/2πε0r, where λ is the linear charge density, ε0 is the permittivity of free space, and r is the distance from the line of charge.

What is the direction of the electric field of an infinite line of charge?

The electric field of an infinite line of charge is always perpendicular to the line of charge, pointing away from positive charges and towards negative charges.

How does the electric field of an infinite line of charge change with distance?

The electric field of an infinite line of charge follows an inverse relationship with distance, meaning that as the distance from the line of charge increases, the electric field decreases.

What are some real-life examples of an infinite line of charge?

An infinite line of charge is a theoretical concept and does not exist in real life. However, it can be approximated in certain situations, such as a long, straight wire with a uniform charge distribution or the edge of a charged plate that is significantly longer than its width.

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