3. Consider the electric potential V generated by two pairs of positive and negative point charges of charge values +g as depicted in the figure: V(b,r,0) The precise form of this potential is given by 1 1 V = 9 + r - 2br cos 0 +r2 + 2br cos 0 1 1 P+r2 - 2br sin 0 2+r2 + 2br sin 0 Show by expressing the function above as a power series expansion in b about b = 0 that in the limit b«r the function is approximately equal to V = (3qb /r) cos(20). This is a form of olontria guedrunole
3. Consider the electric potential V generated by two pairs of positive and negative point charges of charge values +g as depicted in the figure: V(b,r,0) The precise form of this potential is given by 1 1 V = 9 + r - 2br cos 0 +r2 + 2br cos 0 1 1 P+r2 - 2br sin 0 2+r2 + 2br sin 0 Show by expressing the function above as a power series expansion in b about b = 0 that in the limit b«r the function is approximately equal to V = (3qb /r) cos(20). This is a form of olontria guedrunole
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Transcribed Image Text:3. Consider the electric potential V generated by two pairs of positive and negative point
charges of charge values +g as depicted in the figure:
V(b,r,0)
The precise form of this potential is given by
1
1
V = 9
+ r - 2br cos e
+r2 + 2br cos 0
1
1
P+r2 - 2br sin 0
62 +r2 + 2br sin
Show by expressing the function above as a power series expansion in b about b = 0 that
in the limit b«r the function is approximately equal to V = (3qt /r) cos(20). This is a
form of electric quadrupole.
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