The electric potential difference is the electric potential energy per unit charge
Explanation:
First of all, we define the concept of electric potential. The electric potential is a measure of the gradient of the electric field at a certain point of the space. The electric potential at a distance [tex]r[/tex] from a positive charge of magnitude [tex]q[/tex] is given by
[tex]V(r) = \frac{kq}{r}[/tex]
where k is the Coulomb's constant.
Now we can define the electric potential energy and the electric potential difference:
- Electric potential energy is the energy possessed by a charge due to the presence of an electric field. For a charge of magnitude [tex]q[/tex] immersed in an electric field, its potential energy is given by [tex]U=qV[/tex], where V is the electric potential at the location of the charge.
- The electric potential difference is simply the difference in electric potential between two points in the space. For instance, if the potential at point A is V(A) and the potential at point B is V(B), then the potential difference is [tex]\Delta V = V(A)-V(B)[/tex]
The electric potential energy is also defined as the work done on a charge q moved through a potential difference of [tex]\Delta V[/tex]. Consequently, the potential difference [tex]\Delta V[/tex] represents the work per unit charge done, i.e. the work done when moving a unitary charge through a potential difference [tex]\Delta V[/tex].
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