Hi,

I am so stuck with this and I have the feeling that its a simple thing I'm just not realizing.

I have a line charge stretching along the x axis from 0 to a, and from 2a to 3a. with a charge density of [tex]\lambda[/tex] in each region. I have to find what the electric field is at a distance of r<3a along the x axis. I have to show that

E(r) = [[tex]\lambda[/tex]a/4[tex]\pi[/tex][tex]\epsilon[/tex]].( 1/[r(r-a)] + 1/[(r-3a)(r-2a)] )

{sorry about the greek letters being too high, i don't mean 4 to the power pi.epsilon}.

Attempt at solution:

What I thought might be the way to think of is to split the charge up into infinitesimal elements and integrate along from 0 to a, adding up the field at the distance r due to each charge element, then doing the same from 2a to 3a.

But, i just cannot seem to get started. My problem seems to be with the distances (the r's and the a's).

I've started off by saying [tex]\lambda[/tex] = dQ/dr

and dE = dQ/(4[tex]\pi[/tex].[tex]\epsilon[/tex].r

But then i am just confused, this has been doing my head in all night now.

Can anyone help? very much appreciated.

thanks.

PS. if you think i haven't given enough detail or a good enough attempt at solution please say so if you aren't going to reply because of it. I only need a nudge in the right direction anyway I think. cheers.

DIAGRAM: the x's are to show where the charge is spread over, the full stops are empty space.

xxxxxxxxxx..............xxxxxxxxxx........

|---------|---------|---------|----->x

0............a.............2a..........3a

I am so stuck with this and I have the feeling that its a simple thing I'm just not realizing.

I have a line charge stretching along the x axis from 0 to a, and from 2a to 3a. with a charge density of [tex]\lambda[/tex] in each region. I have to find what the electric field is at a distance of r<3a along the x axis. I have to show that

E(r) = [[tex]\lambda[/tex]a/4[tex]\pi[/tex][tex]\epsilon[/tex]].( 1/[r(r-a)] + 1/[(r-3a)(r-2a)] )

{sorry about the greek letters being too high, i don't mean 4 to the power pi.epsilon}.

Attempt at solution:

What I thought might be the way to think of is to split the charge up into infinitesimal elements and integrate along from 0 to a, adding up the field at the distance r due to each charge element, then doing the same from 2a to 3a.

But, i just cannot seem to get started. My problem seems to be with the distances (the r's and the a's).

I've started off by saying [tex]\lambda[/tex] = dQ/dr

and dE = dQ/(4[tex]\pi[/tex].[tex]\epsilon[/tex].r

^{2}) = [tex]\lambda[/tex]dr/(4[tex]\pi[/tex].[tex]\epsilon[/tex].r^{2})But then i am just confused, this has been doing my head in all night now.

Can anyone help? very much appreciated.

thanks.

PS. if you think i haven't given enough detail or a good enough attempt at solution please say so if you aren't going to reply because of it. I only need a nudge in the right direction anyway I think. cheers.

DIAGRAM: the x's are to show where the charge is spread over, the full stops are empty space.

xxxxxxxxxx..............xxxxxxxxxx........

|---------|---------|---------|----->x

0............a.............2a..........3a

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