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Electric Potential
PH 203
Professor Lee Carkner
Lecture 7
Potential

U = Vq

V = ∫ E ds
For a point charge (q):
V = (1/4pe0)(q/r)
Groups of Charges
Since energy is a scalar, potential is too

The potential at a given point is the
algebraic sum of the effects of each
charge that acts on the point
Where V = kq/r (for a point charge), and
each charge has its own q and r
Energy Between Charges

U = q2V = kq1q2/r
This potential energy is relative to an infinite
separation

Or separate them, if they have opposite charge
Systems of Charge

 Find the energy for each charged paired with every other
charge
 We generally solve for the external work

 If the charges have opposite signs, it takes negative work to
bring them together
They will do it themselves
Potential from Dipole

V = k[(q/r(+)) + (-q/r(-))]
If the distance between the
charges is small and if the point of
interest is at an angle q to the
dipole moment,
V = (k p cos q )/ r2
where p = qd, the dipole moment
Continuous Distribution

The potential from each is just
V = k dq / r

V = k ∫ dq / r
We need expressions for dq and r that we can
integrate
Potential from Line

 The charge: dq = l dx

 r = (x2 + d2)½
 Integrating from x = 0 to x = L
V = (kl) ∫ (1 / (x2 + d2)½ )
V =(kl) ln [(L + (L2 + d2)½ ) / d]
 where “ln” is the natural log
Potential from Disk

 Our charge element is a ring of radius R’
and width dR’
 Its charge is s times the ring’s area:
 dq = s(2pR’)(dR’)

 r = (z2 + R’2)½

V = s/2e0 ∫ R’dR’/((z2 + R’2)½)
V = s/2e0 ((z2 + R2)½ - z)
Next Time
Read 25.1-25.4
Problems: Ch 24, P: 16, 69, 70, Ch 25, P:
4, 8
Test #1 is next Monday
Covers Chapters 21-25
Multiple choice and problems
Equations and constant provided
Sample equation sheet on web page
If a charged particle moves along an
equipotential line (assuming no other
forces),
A)
B)
C)
D)
E)
Its potential energy does not change
No work is done
Its kinetic energy does not change
Its velocity does not change
All of the above
A positive particle moves with the field.
What happens to the potential? : What happens to the
potential energy?
High Potential
E
A)
B)
C)
D)
E)
Increase : Increase
Increase : Decrease
Decrease : Decrease
Decrease : Increase
Stay the same : Stay the same
+
Low Potential
A positive particle moves against the field.
What happens to the potential? : What happens to the
potential energy?
High Potential
E
A)
B)
C)
D)
E)
Increase : Increase
Increase : Decrease
Decrease : Decrease
Decrease : Increase
Stay the same : Stay the same
+
Low Potential
A negative particle moves with the field.
What happens to the potential? : What happens
to the potential energy?
High Potential
E
A)
B)
C)
D)
E)
Increase : Increase
Increase : Decrease
Decrease : Decrease
Decrease : Increase
Stay the same : Stay the same
Low Potential
A negative particle moves against the field.
What happens to the potential? : What happens
to the potential energy?
High Potential
E
A)
B)
C)
D)
E)
Increase : Increase
Increase : Decrease
Decrease : Decrease
Decrease : Increase
Stay the same : Stay the same
Low Potential