Question

How is electric potential energy related to electric potential?

Answer 1

Electric potential energy and electric potential are closely related concepts in the field of electrostatics. They both describe different aspects of how charges interact within an electric field.

Electric Potential Energy:
Electric potential energy (U) is the energy associated with the relative positions of electric charges in an electric field. It represents the work that needs to be done to move a charge from one point to another against the electric field. The formula for electric potential energy between two point charges q1 and q2 separated by a distance r is given by Coulomb's law:


=

⋅

1
⋅

2

U=
r
k⋅q
1
    ​

⋅q
2
    ​

    ​


Where:


k is Coulomb's constant (
8.9875
×
1
0
9
 
N m
2
/
C
2
8.9875×10
9
N m
2
/C
2
),

1
q
1
    ​

 and

2
q
2
    ​

 are the magnitudes of the charges,

r is the distance between the charges.
Electric Potential:
Electric potential (V), often referred to simply as potential, is a scalar quantity that describes the electric potential energy per unit charge at a given point in an electric field. It's a measure of how much electric potential energy a unit positive charge would have if placed at that point. The unit of electric potential is the volt (V).

Mathematically, electric potential (

V) is defined as the ratio of electric potential energy (

U) to the charge (

q) placed at a specific point:


=


V=
q
U
    ​


For a point charge

Q creating an electric field at a distance

r away from it, the electric potential due to that point charge is given by:


=

⋅


V=
r
k⋅Q
    ​


In this formula,

V is the electric potential at a distance

r from the charge

Q, and the rest of the symbols have the same meanings as before.

To summarize, electric potential energy represents the work required to move charges within an electric field, while electric potential describes the potential energy per unit charge at a specific point in the electric field. The relationship between them lies in the fact that electric potential is a measure of the electric potential energy per unit charge.