1. Find the exact equation for v(2), the potential on the z axis. 2. Use the binomial expansion and the assumption that z >d to find a formula for v(2) in the form ve) = (1+ +) kq V(z) - A2 22 That is, find the coefficients A, and A2. (As a check, when d → 0, you should get a familiar formula.) 3. In Chapter 3.4 of Griffiths, he derives the formula 1 1 E) ) P,(cos a) JU
1. Find the exact equation for v(2), the potential on the z axis. 2. Use the binomial expansion and the assumption that z >d to find a formula for v(2) in the form ve) = (1+ +) kq V(z) - A2 22 That is, find the coefficients A, and A2. (As a check, when d → 0, you should get a familiar formula.) 3. In Chapter 3.4 of Griffiths, he derives the formula 1 1 E) ) P,(cos a) JU
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Transcribed Image Text:2 Monopole Expansion
For a point charge q at z = d,
1. Find the exact equation for v(2), the potential on the z axis.
2. Use the binomial expansion and the assumption that > d to find a
formula for v(2) in the form
kq
A1
A2
V(z) -
1+
22
That is, find the coefficients A, and A2. (As a check, when d → 0, you
should get a familiar formula.)
3. In Chapter 3.4 of Griffiths, he derives the formula
1
1
P,(cos a)
JU
n=0
where a is the angle between r and r' and r' <r. Equations for P, are
given on page 142.
Based on this, the potential due to a point charge at r' at any location in
space where r > r' can be written as
00
kq
V =
kq
E:) P.(cos a)
JU
n=0
Show that this formula applied to the problem of finding v(2) due to a
point charge q at z
part 2. of this problem.
= d gives the same result for A1 and A2 as found in
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