Strength of an Electric Field

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

    1. The problem statement, all variables and given/known data
    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


    2. Relevant equations
    E = -grad(V)


    3. 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!
     
  2. jcsd
  3. The electric field is a vector field. The potential is a scalar field.
     
  4. 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?
     
  5. Given some arbitrary scalar field V = V(x,y), how would you write down its gradient (in Cartesian coordinates)?
     
  6. V = partial x + partial y?
    Well, grad V = partial x + partial y
     
  7. I think you need to read some vector calculus again.

    [tex]\nabla V = \frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j}[/tex]

    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.
     
    Last edited: Apr 29, 2007
  8. ah ****... i'm stupid..... thx :P
     
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