Electric potential and potential energy
Imagine a positive test charge, Qo, in an external electric field, E(x,y,z) <- it’s a vector field
what is the potential energy, U(x,y,z) of the charge in this field?
- Must define where in space U(x,y,z) is zero, perhaps at infinity (for charge distributions that are finite)
- U(x,y,z) is equal to the work you have to do to take Qo from where U is zero to point (x,y,z)
define V(x,y,z) via U(x,y,z) = QoV(x,y,z)
U depends on what Qo is, but V is independent of Qo (which can be + or -)
V(x,y,z) is the electric potential associated with E(x,y,z)
- V(x,y,z) is a scalar field