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Electron Force and Electric Field 
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#1
Jan1811, 01:51 AM

P: 9

1. The problem statement, all variables and given/known data
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) 2. Relevant equations 3. The attempt at a solution Sorry I couldnt provide any start to this problem, kind of hit a mental block. A jump start would be much appreciated. 


#2
Jan1811, 06:41 AM

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P: 6,683

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
Jan1811, 07:06 AM

P: 1,135

are you familiar with calculus physics?



#4
Jan1811, 12:38 PM

P: 9

Electron Force and Electric Field
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. Electric Field if I use the first equation I'm not quite sure what I would replace all the variables with.



#5
Jan1811, 01:24 PM

P: 1,135

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
Jan1811, 03:39 PM

P: 9

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. Im sure I'm over complicating this problem. I definitely understand the concept but somethings not clicking.



#7
Jan1811, 05:20 PM

P: 1,135

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 


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