Question

Hi, I'm new to this site and i am struggling to answer a question, can anyone please help me? x

The force in an electrostatic field 'Phi'(x, y, z) has the direction of the gradient of 'Phi'. Calculate grad'Phi' and its value at the point P as indicated. 'Phi'(x, y, z) = (x − 1)2 − (y + 1)2, P = (4,−3, 2).

* 'Phi' - grad operator

Answer 1

the gradient, if i recall, should be the partial derivatives of Phi in this case.

Answer 2

the partials generate numbers for the normal to the surface for any given point.\[grad\ Phi=<\frac{\delta\ Phi}{\delta\ x},\frac{\delta\ Phi}{\delta\ y}\frac{\delta\ Phi}{\delta\ z}>\]

Phi (x,y,z) = (x-1)^2 - (y+1)^2

Phi{x} = 2(x-1)
Phi{y} = -2(y+1)
Phi{z} = 0

and to reiterate, this is what i recall and is prone to error :)