Electron Force and Electric Field


by Paul2011
Tags: electric, electron, field, force
Paul2011
Paul2011 is offline
#1
Jan18-11, 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/(2π_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.
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
Andrew Mason
Andrew Mason is offline
#2
Jan18-11, 06:41 AM
Sci Advisor
HW Helper
P: 6,591
Quote Quote by Paul2011 View Post
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/(2π_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.
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
cupid.callin
cupid.callin is offline
#3
Jan18-11, 07:06 AM
P: 1,135
are you familiar with calculus physics?

Paul2011
Paul2011 is offline
#4
Jan18-11, 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.
cupid.callin
cupid.callin is offline
#5
Jan18-11, 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
Paul2011
Paul2011 is offline
#6
Jan18-11, 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.
cupid.callin
cupid.callin is offline
#7
Jan18-11, 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


Register to reply

Related Discussions
Electron Force and Electric Field Introductory Physics Homework 3
Electrostatic force,electric field,electric potential,electric flux Introductory Physics Homework 2
Electric field, Electric Potencial, Electric Force, Potential Electric Energy Classical Physics 1
Electron in an Electric Field Advanced Physics Homework 0
electron through electric field Advanced Physics Homework 5