(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(Sorry for the confusing font- I tried to figure out using the latex reference to indicate a vector, but couldn't do it- please view the "superscripted" variable as a vector. Thanks)

A. The electrostatic potential at P arising form a dipole of unit strength at O, oriented in the direction of the unit vector n, is given by V=n[itex]\stackrel{OP\rightarrow}{}[/itex]/r^3, where r=OP and n coincides with the direction of the positive z axis. Find the value of

del^2V

B. Let F be the gravitational field of a mass oriented at the origin O and is expressed by,

F=c[itex]\stackrel{OA\rightarrow}{}[/itex]/r^3

where c is a constant and r is the distance OA.

Find the value of

Curl F

2. Relevant equations

del^2V=d^2v/dx^2+d^2v/dy^2+d^2v/dz^2

the curl of a function involves the determinant of the matrix [i j k; deriv_x deriv_y deriv_z; f_x f_y f_z] (wrote in matlab form)

3. The attempt at a solution

Sorry about putting two problems together- I figured since it is of similar origin, and the problem itself put it as if it is two parts to a problem. If it must be separated, that can be done.

A. I have managed to get to the point where I can get the expression of V= <0,0,1>[itex]\cdot[/itex]<x,y,z> /Magnitude of OP ^3.

Now do I just have to get the 2nd partial derivative of this function based on the three coordinate systems x y and z? I did it but looked pretty ugly (couldn't simplify), and wanted to make sure.

B. For this part, it looked like the function was:

F=c*<x,y,z>/(magnitude of OA)^3

I went through and calculated the curl of this function based on the formula above, but got 0. is this correct?

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# Two problems involving vector calculus-

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