2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: A(z) = { Ao exp(-z/a) z ≥0 0 Z < 0¹ where Ao and a > 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming $(r →∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.
2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: A(z) = { Ao exp(-z/a) z ≥0 0 Z < 0¹ where Ao and a > 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming $(r →∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.
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Can you try to solve the problem and explain it each step. I have a frame work on how i think I need to solve the problem. (use spherical coordiantes and make comments and suggestions as needed.)
1. write the line charge density as a volume charge sensity using delta functions and spherical harmonics.
2. find the potential using the coloumbs integral form. I provided it below.
3. expand the denominator using spherical and legendre expansion.
4. I just need it in integral form and thats it.
Transcribed Image Text:Φ(x)
=
1
4TTEO
J
p(x')
|x - x' |
d³x'
Transcribed Image Text:function.
2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit
length given by:
Ao
A(z) = { db e
exp(-2/a) z≥0
x<0'
where Ao and a > 0 are constants. Using spherical coordinates, find the electrostatic
potential everywhere, assuming Þ(r → ∞) = 0. It is sufficient to express you answer
in terms of definite integrals over r.
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