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Electric Potential Energy
Level : Physics I
Teacher : Kim
Potential Energy Review & Electric Potential Energy
- Potential energy can be thought of as energy stored within a physical system. It is
called potential energy because it has the potential to be converted into other forms of
energy, such as kinetic energy, and to do useful work in the process.
- Gravitational potential energy(Ug); when we lift an object against a restoring force
straight up, we are storing energy in the object by doing work(=applying a force over a
certain distance). Once released, that stored energy will be transferred to kinetic energy
as it falls
Gravitational potential energy is proportional to vertical position ‘h’ => Ug = mgh
- Elastic potential energy(Us); when we stretch or compress an
object attached to a spring, we are storing energy in the
spring+block system by doing work. Once released, the stored
energy will be transferred to kinetic energy.
Fpush
Elastic potential energy is proportional to the position or
displacement squared
𝟏
=> Us= 𝟐 𝒌𝒙²
Electric potential energy(Ue)
- Electric potential energy is the energy stored by an electric charge due to its position in
an electric field
- A test charge +q (a test charge q is always positive!)
positioned near a stationary negatively charged object
will have a certain amount of electric potential energy
- If released the negative charge does ‘work’ on the
positive test charge by pulling(attracting) on it, resulting
in a change in electric potential energy(ΔUe)
- In this case, the electric potential energy will increase
- If the stationary charge is positive, then there will be a
repulsive force between them. The test charge, once
released, will ‘fall’ away(repel).
- In this case, the electric potential energy will decrease
- When we push test charge +q against an electric field of
a charged body, we are storing electric potential energy.
If the charge(+q) is released, it will accelerate in a
direction away(in this case) from the charged body, and
its electric potential energy will transformed into kinetic
energy
- Electric potential energy is inversely proportional to displacement
=> Ue =k
𝑸𝒒
𝒓
(J)
Q1) Calculate the electric potential energy between two oxide(O2-) ions that are separated
by a distance of 4.8×10-3m. *~ 1electron e- = -1.6×10-19C ~*
a) 1.1×10-25(J)
b) 1.9×10-25(J)
c) 2.8×10-25(J)
d) 4.2×10-25(J)
Electric Potential(V) and Potential Difference(ΔV)
- The electrical potential energy per charge is called the electric potential(V)
electric potential = electrical potential energy / charge
=> V =
𝑈𝑒
or Ue = qV
𝑞
- The potential energy per unit charge or electric potential has a unique value at any point
in an electric field
- Note that electric potential(V) and electric potential energy(Ue) is not the same thing.
- The difference in electric potential between two points is called the potential difference
or often called voltage
- The potential difference(∆V ) or voltage is expressed as
ΔV =
𝜟𝑼𝒆
𝒒
𝑸
=k𝒓
- The unit for electric potential is the volt
1 volt = 1 Joule / 1 Coulomb
V=
𝑈𝑒
𝑞
or Ue = qV
V=
𝑈𝑒
𝑞
or Ue = qV
Q2) Find the electrical potential energy as a proton(q=+1.6×10-19C) moves through a
potential difference of 1.5V.
a) 1.2×10-19(J)
b) 2.4×10-19(J)
c) 4.5×10-19(J)
d) 6.3×10-19(J)
Electron Volt
- It is more convenient to express electric energy using electron volt(eV)
- An electron volt(eV) is defined as the energy required to move an electron between two
points that have a difference of potential of 1 volt
=> 1eV = 1.6×10-19J
- We can find the value of 1 electron volt using the Ue = qV
=> Ue = qV = (1.6×10-19C) × ( 1V) = 1.6×10-19eV
- If we express Q4) in electron volt(eV), then
=> 2.4×10-19×
1𝑒𝑉
1.6×10−19 J
= 1.5eV
- This means we would need 1.5eV to move a proton through a potential difference of
1.5V.
+
- When we talk about batteries or cells in terms of voltage, we
are really talking about the difference in potential between the
positive and negative terminals.
_
- Since 'doing' work is equal to the change in potential
energy(U) (whether we are talking about gravitational potential
energy(Ug) or electric potential energy(Ue) )
𝑾 𝜟𝑼
=
𝒒
𝒒
Using W=Fd & F=qE, we can express voltage as
𝜟𝑽 =
=> V=Ed (only when E=constant)
Q3) How much work is required to move a charge of 3C across a potential difference of
9V?
a) 6J
b) 12J
c) 18J
d) 27(J)
Additional Questions
1. Find the change in electrical potential energy as a proton moves through a potential difference
of 1.5V.
a) 1.1×10-19J
b) 2.4×10-19J
c) 4.9×10-19J
d) 6.6×10-19J
2. An alpha particle has a charge of 3.2×10-19C. If it takes 3.84×10-18 J to move the alpha particle
between two points in an electric field, find the potential difference between the two points.
a) 1.3V
b) 4.7V
c) 7.4V
d) 11.9V
3. i) If an object has a charge that contains 5 times that of a proton, then what is the charge on that
object in Coulombs?
a) 2×10-19C
b) 4×10-19C
c) 6×10-19C
d) 8×10-19C
ii) Express the charge of the object in eV.
a) 5eV
b) 7eV
c) 11eV
4. Find the change in electrical potential energy(in electron volts) as
i) a proton moves through a potential difference of 4.5V.
a) 0.9eV
b) 2.3eV
c) 4.5eV
d) 15eV
d) 7.4eV
2-
ii) an oxide(O ) moves through a potential difference of 5V.
a) 3eV
b) 6eV
c) 10eV
d)17eV
5. How much work is required to move a charge of 3C across a potential difference of 9V?
a) 27J
b) 22J
c) 16J
d) 11J