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I'm trying to use Mathematica to get a numerical answer for a physics problem. I define a function $V$ as the sum of three quantities divided by vector norms:

V = (q1 / Norm[r - a] + q2 / Norm[r - b] + q3 / Norm[r - c])

where 

a = {2, 4, -3}
b = {-2, 3, -5}
c = {-3, -3, -3}
r = {x, y, z}

I define a new quantity DelDotV = {D[V, x], D[V, y], D[V, z]} Then I plug in 3, 4, 5, for x, y, and z, and 1, -2, 3 for q1, q2, and q3, respectively to get a numerical value, and I'm returned the following: Output

I can infer that these are derivatives of absolute value functions, but I know for a fact the answer is not {0, 0, 0}, so I'm not really looking for the derivatives of absolute value of a constant. What exactly are these and why are they there?

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  • $\begingroup$ Mathematica assumes all variables are complex. If you apply FullSimplify with the added assumption that your variables are real, then the Abs' will disappear. $\endgroup$
    – bill s
    Jan 18, 2016 at 23:49
  • $\begingroup$ You didn't specify q1, q2, q3. $\endgroup$
    – David G. Stork
    Jan 18, 2016 at 23:53
  • $\begingroup$ Mathematica doesn't like to take derivatives of the Abs function, which Norm is defined in terms of. Instead of Norm[x], use the explicit form Sqrt[Dot[x, x]]. $\endgroup$
    – march
    Jan 19, 2016 at 0:10

1 Answer 1

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Style recommendation: Never use a variable name starting with an upper-case letter as it may conflict with Mathematica's internal naming convention.

myPotential[q1_, q2_, q3_, r_List, a_List, b_List, c_List] := 
   (q1/Sqrt[Dot[r - a, r - a]] + 
    q2/Sqrt[Dot[r - b, r - b]] + 
    q3/Sqrt[Dot[r - c, r - c]]);

myDelDotPotential[q1_, q2_, q3_, r_, a_, b_, c_] := 
   {D[myPotential[q1, q2, q3, r, a, b, c], x], 
    D[myPotential[q1, q2, q3, r, a, b, c], y], 
    D[myPotential[q1, q2, q3, r, a, b, c], z]};

a = {2, 4, -3};
b = {-2, 3, -5};
c = {-3, -3, -3};
r = {x, y, z};

Simplify@myDelDotPotential[q1, q2, q3, r, a, b, c] /. 
 {x -> 3, y -> 4, z -> 5, q1 -> 1, q2 -> -2, q3 -> 3}

$\left\{\frac{5}{189 \sqrt{14}}-\frac{1}{65 \sqrt{65}}-\frac{18}{149 \sqrt{149}},\frac{1}{189 \sqrt{14}}-\frac{21}{149 \sqrt{149}},\frac{5 \sqrt{\frac{2}{7}}}{189}-\frac{8}{65 \sqrt{65}}-\frac{24}{149 \sqrt{149}}\right\}$

N@%

$\{-0.00473458, -0.0101321, -0.0143207\}$

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