A field describes how quantities are distributed in space

Two types exist: Scalar fields or vector fields; As in this example, electric scalar potential V and electrostatic vector field E, respectively

Electromagnetic fields are postulated to exist via observable phenomena, e.g., via the Lorentz Force:

    \[F=q(E + v * B)\]

Plot notables:

  • Light colors: “high V”; Dark colors: “low V
  • Contour lines represent equipotential surfaces
  • E points from regions of high to low potential (i.e., regions of higher energy to lower energy)
  • Since E is an electrostatic field, \nabla*E=0, it can be written as E=-\nabla{V}

E: vector plot

V: contour plot

Evaluation of E and V at every point in the two-dimensional (x,y) space

Reference Equations

    \[ V(x,y,z) = 2x^2 - 2y^2 (V) \]

    \[ E(x,y,z) = -4x\hat{x} + 4y\hat{y} (V/m) \]