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forty
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A line charge of uniform density [tex]\lambda[/tex] forms a semi-circle of radius R0. Determine the magnitude and direction of the electric field intensity at the center of the semi-circle.
I won't bother with uploading a picture I'm pretty sure you can picture this without.
My trouble with this is I'm unsure whether I need to do a double integral.
So here is my working.
E = (1/4[tex]\pi[/tex][tex]\epsilon[/tex]) q/r2 r
As the problem is symmetric only the cos([tex]\theta[/tex]) components add. So for a small piece of charge dq
Ei = (1/4[tex]\pi[/tex][tex]\epsilon[/tex]) dq/R02 cos([tex]\theta[/tex])
Now for this I have to sum up all the dq's but they are also all have a different angle. So do I do an integral for theta from -[tex]\pi[/tex]/2 to [tex]\pi[/tex]/2 ?
Anyway the answer I get is [tex]\lambda[/tex]/2[tex]\epsilon[/tex]R0
Any help with this would be greatly appreciated.
P.S. I'm new to latex.
I won't bother with uploading a picture I'm pretty sure you can picture this without.
My trouble with this is I'm unsure whether I need to do a double integral.
So here is my working.
E = (1/4[tex]\pi[/tex][tex]\epsilon[/tex]) q/r2 r
As the problem is symmetric only the cos([tex]\theta[/tex]) components add. So for a small piece of charge dq
Ei = (1/4[tex]\pi[/tex][tex]\epsilon[/tex]) dq/R02 cos([tex]\theta[/tex])
Now for this I have to sum up all the dq's but they are also all have a different angle. So do I do an integral for theta from -[tex]\pi[/tex]/2 to [tex]\pi[/tex]/2 ?
Anyway the answer I get is [tex]\lambda[/tex]/2[tex]\epsilon[/tex]R0
Any help with this would be greatly appreciated.
P.S. I'm new to latex.
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