In electrostatics, the potential at a point in space due to a point charge is a fundamental concept. The electric potential at a point is the amount of work done in bringing a unit positive charge from infinity to that point, against the electric field created by the point charge. It is often denoted by the symbol "V."
Mathematically, the electric potential
V at a point in space due to a point charge
Q located at a distance
r away from the point is given by Coulomb's law:
=
⋅
,
V=
r
k⋅Q
,
where:
k is Coulomb's constant (
8.988
×
1
0
9
N m
2
/
C
2
8.988×10
9
N m
2
/C
2
in SI units),
Q is the magnitude of the point charge,
r is the distance between the point charge and the point where you're calculating the potential.
It's important to note that potential is a scalar quantity and has units of volts (V), which is equivalent to joules per coulomb (J/C).
If you have multiple point charges, the total potential at a point due to all those charges is the algebraic sum of the potentials due to each individual charge. This is known as the principle of superposition.
If you're dealing with a collection of point charges, you would add up the potentials due to each charge using the formula above to determine the total potential at a particular point.
Remember that electric potential is a scalar and it doesn't have a direction. It simply tells you the potential energy per unit charge at a given point in the electric field created by the charge(s).
If you need to find the potential difference between two points in an electric field, you can subtract the electric potentials at those points:
Δ
=
final
−
initial
.
ΔV=V
final
−V
initial
.
This potential difference is also known as voltage and is commonly used in circuit analysis and other applications.