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Electric Dipole and Electric Potential.. and binomial approximation!
An electric dipole at the origin consists of two charges +q and -q spaced distance s apart along the y-axis.
a.)Find an expression for the potential V(x,y) at an arbitrary point in the xy-plane.
b.)Use the binomial approximation to simplify your result of part A when s<<x and s<<y.
V=kq1/r1+kq2/r2
binomial approximation: (1+z)n=(1+nz) when z<<1
Solution to a is:
V = kq(1/(x2+(y-s/2)2)1/2)-1/(x2+(y+s/2)2)1/2))
I just have no idea how to make the square root parts into (1 + something small)1/2
I multiplied out, and ended up with (just for the first fraction):
1/(x2+y2+s2/4)-1/2 because i figured the -ys that came from expanding the (y-s/2)2 is small enough to be considered zero.
Just a few hints to send me in the right direction would be awesome!
Homework Statement
An electric dipole at the origin consists of two charges +q and -q spaced distance s apart along the y-axis.
a.)Find an expression for the potential V(x,y) at an arbitrary point in the xy-plane.
b.)Use the binomial approximation to simplify your result of part A when s<<x and s<<y.
Homework Equations
V=kq1/r1+kq2/r2
binomial approximation: (1+z)n=(1+nz) when z<<1
The Attempt at a Solution
Solution to a is:
V = kq(1/(x2+(y-s/2)2)1/2)-1/(x2+(y+s/2)2)1/2))
I just have no idea how to make the square root parts into (1 + something small)1/2
I multiplied out, and ended up with (just for the first fraction):
1/(x2+y2+s2/4)-1/2 because i figured the -ys that came from expanding the (y-s/2)2 is small enough to be considered zero.
Just a few hints to send me in the right direction would be awesome!
