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 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. 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: 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: 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 +q r 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 +q r 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 +q r 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 +q r 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 +q r +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 +q r +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 +q r +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: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram? q1q1 q2q2 r Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB r r A B

q1q1 q2q2 r 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: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram?

q1q1 q2q2 r 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: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram?

q1q1 q2q2 r 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: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram?

q1q1 q2q2 r 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: Similarly at point B we have: q1q1 q2q2 rr r A B x Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram?

q1q1 q2q2 r 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: Similarly at point B we have: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram? q1q1 q2q2 rr r A B x

q1q1 q2q2 r 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: Similarly at point B we have: 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: q 1 =+10nC; q 2 =+5nC; r=10cm. a) What is the electric potential difference (in Volts) between points A and B in the diagram? q1q1 q2q2 rr r A B x

q3q3 r A Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. b) Now suppose another charge q 3 = -4mC moves from point A to point B. How much work (in Joules) is required to move the charge? q1q1 q2q2 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: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. b) Now suppose another charge q 3 = -4mC moves from point A to point B. How much work (in Joules) is required to move the charge? q3q3 r A q1q1 q2q2 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: To get the change in the potential energy, multiply by the amount of charge that is moving: Example 2: 2 charges are initially arranged along a line, as shown. The following values are given: q 1 =+10nC; q 2 =+5nC; r=10cm. b) Now suppose another charge q 3 = -4mC moves from point A to point B. How much work (in Joules) is required to move the charge? q3q3 r A q1q1 q2q2 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: To get the change in the potential energy, multiply by the amount of charge that is moving: 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: q 1 =+10nC; q 2 =+5nC; r=10cm. b) Now suppose another charge q 3 = -4mC moves from point A to point B. How much work (in Joules) is required to move the charge? q3q3 r A q1q1 q2q2 r r B