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| A question on Electric Potential | | |
|  ajinx999 | Sep 24, 2007 11:46am | This is the question:
" Positive charges, each with a magnitude of 'q' are kept at distances x, 3x, 5x, ...(inf) (odd multiple of x) from the origin.
Negative charges, each with a magnitude of 'q' are kept at distances 2x, 4x, 6x, ...(inf) (even multiple of x) from the origin.
All charges are placed on the positive direction of x-axis.
'x' is any positive real number.
What is the net electrostatic potential of the system of charges at the origin?
There is no charge on the origin. The above sequences of charges are infinite. The permittivity of the medium is '(epsilon)'. |
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Sponsor |  disconcision | Sep 24, 2007 2:15pm | p = pi, e = epsilon
potential(origin) = q/4per =
sum_r(kq/r_odd) + sum_r(-kq/r_even) =
q/4pe*(sum_r(1/r_odd) - sum_r(1/r_even) =
q/4pe*(1/x - 1/2x + 1/3x - 1/4x + 1/5x ..)
q/4pex*(1 - 1/2 + 1/3 - 1/4 + 1/5 ..)
= q*ln2/4pex
I'm really rusty so I'd wait for peer review. :) |
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Sponsor | | ntltrmllgnc | Sep 24, 2007 2:42pm | | I think there's a joke here involving the series for sine and cosine. |
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| | ajinx999 | Sep 26, 2007 8:39am | @disconcision:
Your answer is true. I had got that series but I didn't equal it to ln2.
Sorry, previously I wrongly stated about the relationship between ln2 and the given series. |
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| A question on Electric Potential | | |
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