Vectors task concerning electrostatic function

[sky_tm]

vectors 2

The electric intensity of a electrostatic function \[V(x,y,z)\] is \[E = - \nabla V\]

The elecrostatic potential produced by a unit dipole-moment, located at the origin and directed along the y-axis, is given by
\[V(x,y,z) = \frac{y}{{(x^2 + y^2 + z^2 )^{3/2} }}\]

i) Determine the corresponding field-intensity function E.

ii) In what direction, does the potential decreases most rapidly from the point (4,2,4)?

 

[steve10]

Re: vectors 2

This question is not so hard to answer, but it's a little tedious as you have to take the derivatives of V(x,y,z). Well, you have to do this by yourself or you may appeal to Mathematica. I am sure it'll help.

Answer:

i) (-dV/dx,-dV/dy,-dV/dz);
ii) in the direction = (-dV/dx,-dV/dy,-dV/dz) where (x,y,z)=(4,2,4).