Electron Force and Electric Field

In summary, the problem is asking to find the electric field at the origin due to a thin rod with a given linear charge density equation. The approach is to break the rod into small discs and use the formula for electric field of a point charge to find the electric field at the origin due to each disc, and then integrate from the origin to the end of the rod.
  • #1
Paul2011
9
0

Homework Statement



A thin rod runs along the x-axis from the origin to
x = l. Its linear charge density (C/m) is given by
λ = λ_0(x/l)^2 sin (x/lπ), where λ_0 is a constant.
Show that at the origin,

E(0)=〖-λ〗_0/(2π²€_0l)

Homework Equations





The Attempt at a Solution



Sorry I couldn't provide any start to this problem, kind of hit a mental block. A jump start would be much appreciated.
 
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  • #2
Paul2011 said:

Homework Statement



A thin rod runs along the x-axis from the origin to
x = l. Its linear charge density (C/m) is given by
λ = λ_0(x/l)^2 sin (x/lπ), where λ_0 is a constant.
Show that at the origin,

E(0)=〖-λ〗_0/(2π²€_0l)

Homework Equations





The Attempt at a Solution



Sorry I couldn't provide any start to this problem, kind of hit a mental block. A jump start would be much appreciated.
What law applies?

Think of the rod as a series of thin disks of thickness dx. Calculate the electric field of that disk as a function of x along the entire length of the rod.

AM
 
  • #3
are you familiar with calculus physics?
 
  • #4
Ok, after reading what you have had to say I am a little embarrassed to say that I am not grasping the whole thing. I under stand that the rod can be visualized as a bunch of discs which would run from the origin to x=l, which I wrote on my coordinate plane as (l,0). the end points are from (0,0) to (l,0). So I know my bounds would run from 0 to l. And also, the thickness of the disc is dx. What I'm trying to understand is where does the given equation,λ = λ_0(x/l)^2 sin (x/lπ) come into the picture. https://www.physicsforums.com/library.php?do=view_item&itemid=2" if I use the first equation I'm not quite sure what I would replace all the variables with.
 
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  • #5
λ is the density

suppose you are considering any dics of negligible thickness dx at distance x from origin.
how will you find the charge in that disc?

and a little hint: as rod is thin, you may take the discs to be acting like small point charges and instead of using Electric field formula of disc, use formula of point charge
 
  • #6
If I use the point charge formula F= (kq_1q_2)/r^2 then my r would be from origin to l so total distance of l. And I would have to add them up from the origin to x=l. I am sure I'm over complicating this problem. I definitely understand the concept but somethings not clicking.
 
  • #7
you are not over complicating it.

lets go step wise:
1. assume a section dx at distance x from origin
2. find charge in it.
3. find the electric field dE at origin due to that charge
4. Integrate it from x=0 to x=l
 

1. What is the difference between electron force and electric field?

Electron force refers to the attraction or repulsion between two charged particles, while electric field refers to the space around a charged particle where its influence can be felt.

2. How is the strength of an electric field measured?

The strength of an electric field is measured using a unit called volts per meter (V/m). This unit represents the amount of force exerted on a charged particle per unit of electric charge.

3. How do electron force and electric field affect the movement of electrons?

Electron force and electric field determine the direction and speed of electron movement. Charged particles will be attracted to areas with a stronger electric field, and repelled from areas with a weaker electric field.

4. How are electron force and electric field related to each other?

Electron force and electric field are closely related. The strength of the electric field determines the force exerted on a charged particle, and the direction of the electric field determines the direction of the force.

5. How can electron force and electric field be manipulated?

Electron force and electric field can be manipulated by changing the amount and distribution of charged particles in a given area. This can be done through the use of conductors, insulators, and electrically charged objects.

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