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Vector calculus question relating to electrical dipoles (more of a math question)

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jsund323
#1
Dec12-11, 10:24 PM
P: 1
The potential for an ideal electric dipole is given by

V(x,y,z)= pz/(4π ε0(x+y^2+z^2))

In rectangular, spherical, and cylindrical coordinates:
a) Find the electric field, E(x,y,z)= -∇V. (E is a vector, can't figure out how to denote that on my computer).

b) By direct Calculation find ∇E and ∇XE (E is still vector)

this isn't really a physics question and more a vector calc question, but maybe someone is feeling up to flexing their spherical and cylindrical coordinate skills.
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cragar
#2
Dec12-11, 11:14 PM
P: 2,464
the gradient in rectangular coordinates should be straight forward, take the derivatives of the components and then add them up. And then for cylindrical and spherical coordinates change x,y , z in terms of (rho)(theta(phi) or the appropriate variables and then take the gradient. but in cylindrical and spherical you have to be more careful with the gradient because their are terms in front, this should be on the inside cover of your book.


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