Calculating Field?

Question

What is the magnitude of the electric field a the point (3.00i – 200j + 400k) m if the electric potential is given by V = 2.00xyz^2, V is in Volts and x, y, and z are in meters.

I'm lost need some work!

sorry guys typo that should be 3.00i – 2.00j + 4.00k

Answer 1

The vector components of the electric field are

Ex = ∂V/∂x, Ey = ∂V∂y, and Ez = ∂V/∂z

Taking these derivatives gives

Ex = 2.00*y*z^2
Ey = 2.00*x*z^2
Ez = 4.00*x*y*z

Plug in the values for x y and z at the point given:

x = 3.00, y = -200 and z = 400 (is there a decimal point missing in those last two numbers?). Anyway, you can plug in the right numbers to get the values of the field components.

After getting the vector components of the field, find the magnitude from

E = √[Ex^2 + Ey^2 + Ez^2]