1. Chapter 17 Electric Potential

2. Question 1 answer

3. Question 2 Answer

4. Question 3 Answer

5. Objectives: The students will be able to: Determine the magnitude of the potential at a point a known distance from a point charge or an arrangement of point charges. State the relationship between electric potential and electric field and determine the potential difference between two points a fixed distance apart in a region where the electric field is uniform. Explain what is meant by an electric dipole and determine the magnitude of the electric dipole moment between two point charges.

6. 17.5 Electric Potential Due to Point Charges The electric potential due to a point charge can be derived using calculus. (17-5)

7. 17.5 Electric Potential Due to Point Charges The potential in this case is usually taken to be zero at infinity; this is also where the electric field (E=kQ/r 2 ) is zero. The result is (17-5) Where k = 8.99 x 10 9 Nm 2 /C 2. V is the absolute potential at a distance r from the charge Q, where V = 0 at r = ∞, or think of V as the potential difference between r and infinity.

8. 17.5 Electric Potential Due to Point Charges These plots show the potential due to (a) positive and (b) negative charge.

9. 17.5 Electric Potential Due to Point Charges Notice that the potential V decreases with the first power of the distance, whereas the electric field decreases as the square of the distance.

10. 17.5 Electric Potential Due to Point Charges Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector.

11. Example 17-4 page 477: Determine the potential at a point 0.50 m (a) from a +20 μC point charge, (b) From a -20 μC point charge.

12. Example 17-4 page 477: Determine the potential at a point 0.50 m (a) from a +20 μC point charge, (b) From a -20 μC point charge.

13. Example 17-5 page 477: Work done to bring two Positive charges close together. What minimum work must be done by an external force to bring a charge q = 3.00 μC from a great distance away (take r = ∞) to a point 0.500m from a charge Q = 20.0 μC?

14. Example 17-5 page 477: Work done to bring two Positive charges close together. What minimum work must be done by an external force to bring a charge q = 3.00 μC from a great distance away (take r = ∞) to a point 0.500m from a charge Q = 20.0 μC?

15. Example 17-5 page 477: Work done to bring two Positive charges close together. What minimum work must be done by an external force to bring a charge q = 3.00 μC from a great distance away (take r = ∞) to a point 0.500m from a charge Q = 20.0 μC?

16. Example 17-6: Potential above two charges. Calculate the electric potential (a) at point A in Fig. 17-10 Due to the two charges shown, and (b) at point B. This is The same situation as Example 16-9, Fig. 16-28, where we Calculated the electric field at these points.

17. Example 17-6: Potential above two charges. Calculate the electric potential (a) at point A in Fig. 17-10 Due to the two charges shown, and (b) at point B. This is the same situation as Example 16-9, Fig. 16-28, where we calculated the electric field at these points.

19. Figure 17-11 Example 17-7 Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (a)Which set has a Positive potential energy?

20. Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (a)Which set has a Positive potential energy?

21. Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (a)Which set has a Positive potential energy? Set (iii) has a positive potential energy because the charges have the same sign.

22. Figure 17-11 Example 17-7 Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (b) Which set has the most negative potential energy?

23. Figure 17-11 Example 17-7 Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (b) Which set has the most negative potential energy? Both (i) and (ii) have opposite signs of charge and negative PE. Because r is smaller in (i), the PE is most negative for (i).

24. Figure 17-11 Example 17-7 Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (c) Which set requires the most work to separate the charges to infinity? Assume the charges all have the same magnitude.

25. Figure 17-11 Example 17-7 Potential energies. Consider the three pairs of charges. Call them Q 1 and Q 2. (c) Which set requires the most work to separate the charges to infinity? Assume the charges all have the same magnitude. Set (i) will require the most work for separation to infinity. The more negative the potential energy, the more work required to separate the charges and bring PE up to zero (r = ∞).

26. 17.6 Potential Due to Electric Dipole; Dipole Moment The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly. Two equal point charges Q, of opposite sign, separated by a distance l, are called an electric dipole. See figure to the left.

27. 17.6 Potential Due to Electric Dipole; Dipole Moment Approximation for potential far from dipole: (17-6a)

28. Or, defining the dipole moment p = Ql, (17-6b) 17.6 Potential Due to Electric Dipole; Dipole Moment

29. Table 17-2 Dipole Moments of Selected Molecules

30. Homework Chapter 17 #18, 19, 24, 26

31. Closure Kahoot 17-5 and 17-6