# Electric Potential Energy or Potential Difference (Voltage) ```Electric Potential Energy or
Potential Difference (Voltage)
• Recall the idea of Gravitational Potential
Energy: lifting an object against gravity
requires work, and energy is transferred to
the object.
• The same idea can be used to explain
electric potential.
• Consider two charged objects found
between two charged plates, each
experiences a force to the right of
magnitude: F = qE
B
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1
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Fe
Fe
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2
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A
B
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1
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Fe
Fe
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2
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A
Object 1: Suppose it is free
to move through a distance
d, from B to A. Since a
certain force acts on an
object through a distance d,
a certain amount of work is
done on the charged object.
W = Fed
Object 2: We could force this charge to the
left if we grabbed it and exerted a force on it
throughout the distance d. This would mean
we would have to do work on the charge.
(W = Fed)
* If work is done on a charge when it freely moves
or is forced to move from one point to another,
these two points are said to differ in their electric
potential, The amount of work done is a measure
of this difference in electric potential or electric
potential energy.
Potential Difference (V)
• The potential difference between two points in an electric
field is the amount of work done per unit of charge as a
charge is moved between two points.
• Mathematically:
• Potential Difference = Work Done
Charge
W
V
q
Rearrange to W = qV
• The volt – one volt is the potential
difference between two points in an electric
field when one joule of work is done in
moving a charge of 1 C between these
points.
Relationship between Potential
Difference (Voltage) and Electric Field
Strength
• We have seen that:
W
V
units are J/C
q
Remember 1 J = 1 Nm
So 1 V = 1 Nm/C
This gives us that 1 V/m = 1 N/C
• so Volts / metre – Newtons / Coulomb =
units of electric field strength (E)
• Thus, the electric field strength which we
previously expressed in units of N/C can
also be expressed in units of volts / metre.
• This leads us to the formula
V
E
r
r = distance (m)
• When E is expressed in volts / metre it gives
the charge or difference in electric potential
energy per unit of distance, and is called the
potential gradient of the electric field.
Sample Problem
• A charged particle of mass 4.0 x 10-15 kg is
balanced between charged plates. The
battery is rated at 5000 V and the plates are
4.0 cm apart.
- - - - - - - - - - - Fe
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Fg
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Find
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electric Field Strength
electric force on the particle
amount of charge on the object
number of elementary charges on the
particle
• solution
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