What Is the X-Component of the Electric Field from a Given Potential?

[Ron Burgundy]

Homework Statement

The electric potential in a certain region of space is given by V(x,y,z) = αxy + β, in units of volts, where α = 3.29 V/m2 and β = 6.38 V are constants. What is the x-component of the electric field at a point P = (4.50, 5.00, 4.50), where the coordinates are given in meters?

Homework Equations

E = -gradient * V

The Attempt at a Solution

Gradient = (fx ,fy ,fz )
Gradient = (3.29y , 3.29x ) = (3.29*5 , 3.29*4.5) = (16.45, 14.805)

V = 3.29xy + 6.38 = 3.29(4.5)(5) + 6.38 = 80.405

E = - (16.45, 14.805)*(80.405)

I got that the x-component is -1322.66 V/m. This is wrong and I can't figure out why.

 

[klouchis]

Your answer is wrong because after you computed the gradient of the potential you multiplied your result by the potential again. The math you did is below:

E=-grad(V)*V

Your result for grad(V) is correct, the x component (with a negative sign) of the gradient of V will give you the x component of the electric field.

The answer should be found using the following definition of the electric field at the point of interest:

E=-grad(V) = -(16.45, 14.805)