Calculating Electric Field Strength from Potential in a 2D Region

[boozi]

Hello. This is my first time here, so let me know if I'm doing anything wrong "posting-wise."

Homework Statement

The electric potential in a region of space is V= (260 x^2 - 180 y^2) V, where x and y are in meters.

What is the strength of the electric field at (2.00 m, 3.00 m) ?
x = 2.00 m
y = 3.00 m

Homework Equations

E = -grad(V)

The Attempt at a Solution

E = -grad(V) = -(520(x) - 360(y)) = -(-40) = 40

I feel really stupid because it's not the right answer... What am I doing wrong? Thanks in advance!

 

[neutrino]

E = -grad(V) = -(520(x) - 360(y)) = -(-40) = 40

The electric field is a vector field. The potential is a scalar field.

 

[boozi]

I'm still a bit confused... Well, I have to take into account the direction, too, but... How do I account for it in the equation?

 

[neutrino]

Given some arbitrary scalar field V = V(x,y), how would you write down its gradient (in Cartesian coordinates)?

 

[boozi]

V = partial x + partial y?
Well, grad V = partial x + partial y

 

[neutrino]

V = partial x + partial y?
Well, grad V = partial x + partial y

I think you need to read some vector calculus again.

$$\nabla V = \frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j}$$

The gradient tells you the direction in which the scalar field, V, is increasing the fastest (at some point). Since a direction is involved it is a vector. But remember, the question asks for the strength of the field, which is the magnitude of the field.

 

[boozi]

ah ****... I'm stupid... thanks :P