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Physics 6B
Electric Potential and
Electric Potential Energy
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Electric Potential
Measured in Volts
Electric Potential Energy
Measured in Joules)Coulomb
Joule1Volt1(
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Electric Potential
Measured in Volts
Represents the energy it takes to move exactly 1 Coulomb of charge from one place to another in an electric field.
Electric Potential Energy
Measured in Joules
Represents the energy it takes to move a charge from one place to another in an electric field.
)Coulomb
Joule1Volt1(
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Electric Potential
Measured in Volts
Represents the energy it takes to move exactly 1 Coulomb of charge from one place to another in an electric field.
Formula for potential near point charge Q:
Electric Potential Energy
Measured in Joules
Represents the energy it takes to move a charge from one place to another in an electric field.
Formula for the potential energy of 2 point charges Q and q:
)Coulomb
Joule1Volt1(
r
kQV r
kQqUelec
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Electric Potential
Measured in Volts
Represents the energy it takes to move exactly 1 Coulomb of charge from one place to another in an electric field.
Formula for potential near point charge Q:
Notes:This is not a vector. Use the sign of the charge to determine the sign of the potential.
Potential is defined to be zero when r→∞
We will typically use potential differences that will look like ΔV. Don’t get voltage confused with velocity or volume.
Electric Potential Energy
Measured in Joules
Represents the energy it takes to move a charge from one place to another in an electric field.
Formula for the potential energy of 2 point charges Q and q:
Notes:This is not a vector, so the signs of the charges may be used in the formula.
Potential Energy is always Potential times charge:
)Coulomb
Joule1Volt1(
r
kQV r
kQqUelec
qVUelec
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.+Q
+qr
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
+Q
+qr
r
kQqUelec
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
This represents the amount of energy it would take to move these charges to where they are now, if they started very far apart (r→∞)
+Q
+qr
r
kQqUelec
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
This represents the amount of energy it would take to move these charges to where they are now, if they started very far apart (r→∞)
Like gravitational potential energy, we only really care about the difference in potential energy when the charges move from one arrangement to another. Our formula defines zero potential energy – when r→∞.
+Q
+qr
r
kQqUelec
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
This represents the amount of energy it would take to move these charges to where they are now, if they started very far apart (r→∞)
Like gravitational potential energy, we only really care about the difference in potential energy when the charges move from one arrangement to another. Our formula defines zero potential energy – when r→∞.
Now suppose that charge q is moved closer, so it is a distance r/3 from charge Q.
+Q
+qr
r
kQqUelec
+Q
+qr/3
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
This represents the amount of energy it would take to move these charges to where they are now, if they started very far apart (r→∞)
Like gravitational potential energy, we only really care about the difference in potential energy when the charges move from one arrangement to another. Our formula defines zero potential energy – when r→∞.
Now suppose that charge q is moved closer, so it is a distance r/3 from charge Q.
Now the potential energy is larger (it would take some work to move q closer to Q since they are the same sign).
How much larger is the energy?
+Q
+qr
r
kQqUelec
+Q
+qr/3
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 1: Two point charges
Charges Q and q are separated by distance r.
The potential energy of this arrangement is given by our formula:
This represents the amount of energy it would take to move these charges to where they are now, if they started very far apart (r→∞)
Like gravitational potential energy, we only really care about the difference in potential energy when the charges move from one arrangement to another. Our formula defines zero potential energy – when r→∞.
Now suppose that charge q is moved closer, so it is a distance r/3 from charge Q.
Now the potential energy is larger (it would take some work to move q closer to Q since they are the same sign).
How much larger is the energy?3 times larger than before
+Q
+qr
r
kQqUelec
+Q
+qr/3
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
r
kq
r
kqV 21
A
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
m1.0
C105109
m1.0
C1010109
r
kq
r
kqV
9
CmN99
CmN9
21A
2
2
2
2
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
V1350450900V
m1.0
C105109
m1.0
C1010109
r
kq
r
kqV
CmN
CmN
A
9
CmN99
CmN9
21A
2
2
2
2
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
V1350450900V
m1.0
C105109
m1.0
C1010109
r
kq
r
kqV
CmN
CmN
A
9
CmN99
CmN9
21A
2
2
2
2
Similarly at point B we have:
r2
kq
r2
kqV 21
B
q1 q2r r
r
A
B
x
r2r2xrrx 2222
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
V1350450900V
m1.0
C105109
m1.0
C1010109
r
kq
r
kqV
CmN
CmN
A
9
CmN99
CmN9
21A
2
2
2
2
Similarly at point B we have:
V954318636V
m14.0
C105109
m14.0
C1010109
r2
kq
r2
kqV
CmN
CmN
B
9
CmN99
CmN9
21B
2
2
2
2
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r r
r
A
B
x
r2r2xrrx 2222
q1 q2r
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
A
B
We calculate the potential due to each charge separately, then add them to get the total potential. At point A we get:
V1350450900V
m1.0
C105109
m1.0
C1010109
r
kq
r
kqV
CmN
CmN
A
9
CmN99
CmN9
21A
2
2
2
2
Similarly at point B we have:
V954318636V
m14.0
C105109
m14.0
C1010109
r2
kq
r2
kqV
CmN
CmN
B
9
CmN99
CmN9
21B
2
2
2
2
Thus the potential difference is just 396 Volts (with B at a lower potential than A)
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
a) What is the electric potential difference (in Volts) between points A and B in the diagram?
q1 q2r r
r
A
B
x
r2r2xrrx 2222
q3r
A
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
b) Now suppose another charge q3= -4mC moves from point A to point B. How much work (in Joules) is required to move the charge?
q1 q2
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
r
r
B
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We already have the potential difference from part a).
Here is the calculation: V396V1350V954VVV ABAB
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
b) Now suppose another charge q3= -4mC moves from point A to point B. How much work (in Joules) is required to move the charge?
q3r
A
q1 q2r
r
B
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We already have the potential difference from part a).
Here is the calculation: V396V1350V954VVV ABAB
To get the change in the potential energy, multiply by the amount of charge that is moving:
J6.1V396C104VqU 3ABelec
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
b) Now suppose another charge q3= -4mC moves from point A to point B. How much work (in Joules) is required to move the charge?
q3r
A
q1 q2r
r
B
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We already have the potential difference from part a).
Here is the calculation: V396V1350V954VVV ABAB
To get the change in the potential energy, multiply by the amount of charge that is moving:
J6.1V396C104VqU 3ABelec
The work done on the system is the same as this change in the potential energy. Another way to think about it is that the electric field did -1.6J of work, so the potential energy of the system increased by 1.6J.
Basic rule of thumb:
When the potential energy of the system decreases, positive work is done by the electric force.
When potential energy increases, negative work is done by the electric force (or alternatively, positive work is done on the system by outside forces).
Example 2:2 charges are initially arranged along a line, as shown.The following values are given:q1=+10nC; q2=+5nC; r=10cm.
b) Now suppose another charge q3= -4mC moves from point A to point B. How much work (in Joules) is required to move the charge?
q3r
A
q1 q2r
r
B
