Finding Ex from potential along the x-axis

[aftershock]

Let's say I have the electric potential as a function of x, y, and z: V(x,y,z)

Now I want to find the x component of the electric field along the x-axis: E_x(x,0,0)


I could take the derivative of the potential wrt x and then plug in zero for y and z.

However if I was to plug in zero for y and z in the potential function, and then derive, would that be valid?

 

[tiny-tim]

hi aftershock!

your notation is odd … E = (E_x,E_y,E_z) = (∂V/∂x,∂V/∂y,∂V/∂z)

∂V/∂x means the derivative of V wrt x, keeping y and z fixed, so yes if you fix y = y_o, z = z_o, that would give you the correct value of E_x at (x_o,y_o,z_o)