Ch 25 – Electric Potential

1. Ch 25 – Electric Potential A difference in electrical potentialbetween the upper atmosphere and the ground can cause electrical discharge (motion of charge).

2. Ch 25 – Electric Potential So far, we’ve discussed electric force and fields. Now, we associate a potential energy function with electric force. This is identical to what we did with gravity last semester. gravity electricity ?

3. Ch 25.1 – Electric Potential and Potential Difference • Place a test charge, q0, into an E-field. The charge will experience a force: • This force is a conservative force. • Pretend an external agent does work to move the charge through the E-field. • The work done by the external agent equals at least the negative of the work done by the E-field.

4. Ch 25.1 – Electric Potential and Potential Difference • Let’s introduce a new symbol: • We’re talking about moving charges through some displacement. • The “ds” vector is a little tiny step of displacement along a charge’s path.

5. Ch 25.1 – Electric Potential and Potential Difference • If q0 moves through the E-field by a little step ds, the E-field does some work: • As the E-field performs this work, we say that the potential energy of the charge-field system changes by this amount. • This is the basis for our definition of the potential energy function.

6. Ch 25.1 – Electric Potential and Potential Difference • If q0 moves through the E-field by a little step ds, the E-field does some work:

7. Ch 25.1 – Electric Potential and Potential Difference The change in electrical potential energy of a charge-field system as the charge moves from A to B in the field. The integral accounts for the motion of the charge through a 1-D path. It’s called a “path” or “line” integral.

8. Ch 25.1 – Electric Potential and Potential Difference The change in electrical potential energy of a charge-field system as the charge moves from A to B in the field. Because electric force is conservative, the value of the integral does not depend on the path taken between A and B.

9. Ch 25.1 – Electric Potential and Potential Difference Potential Energy refresher: Potential Energy measures the energy a system has due to it’s configuration. We always care about changes in potential energy – not the instantaneous value of the PE. The zero-point for PE is relative. You get to choose what configuration of the system corresponds to PE = 0. The change in electrical potential energy of a charge-field system as the charge moves from A to B in the field.

10. Ch 25.1 – Electric Potential and Potential Difference • What we’re about to do is different than anything you saw in gravitation. • In electricity, we choose to divide q0 out of the equation. • We call this new function, ΔV, the “electric potential difference.”

11. Ch 25.1 – Electric Potential and Potential Difference • This physical quantity only depends on the electric field. • Potential Difference – the change in potential energy per unit charge between two points in an electric field. • Units: Volts, [V] = [J/C] Potential difference between two points in an Electric Field.

12. Ch 25.1 – Electric Potential and Potential Difference • Do not confuse “potential difference” with a change in “electric potential energy.” • A potential difference can exist in an E-field regardless the presence of a test charge. • A change in electric potential energy can only occur if a test charge actually moves through the E-field. Potential difference between two points in an Electric Field.

13. Ch 25.1 – Electric Potential and Potential Difference • Pretend an external agent moves a charge, q, from A to B without changing its speed. Then: But:

14. Ch 25.1 – Electric Potential and Potential Difference • Units of the potential difference are Volts: • 1 J of work must be done to move 1 C of charge through a potential difference of 1 V.

15. Ch 25.1 – Electric Potential and Potential Difference • We now redefine the units of the electric field in terms of volts. E-field units in terms of volts per meter

16. Ch 25.1 – Electric Potential and Potential Difference • Another useful unit (in atomic physics) is the electron-volt. • One electron-volt is the energy required to move one electron worth of charge through a potential difference of 1 volt. • If a 1 volt potential difference accelerates an electron, the electron acquires 1 electron-volt worth of kinetic energy. The electron-volt

17. Quick Quiz 25.1 Points A and B are located in a region where there is an electric field. How would you describe the potential difference between A and B? Is it negative, positive or zero? Pretend you move a negative charge from A to B. How does the potential energy of the system change? Is it negative, positive or zero?

18. Ch 25.2 – Potential Difference in a Uniform E-Field Let’s calculate the potential difference between A and B separated by a distance d. Assume the E-field is uniform, and the path, s, between A and B is parallel to the field.

19. Ch 25.2 – Potential Difference in a Uniform E-Field Let’s calculate the potential difference between A and B separated by a distance d. Assume the E-field is uniform, and the displacement, s, between A and B is parallel to the field. 1

20. Ch 25.2 – Potential Difference in a Uniform E-Field The negative sign tells you the potential at B is lower than the potential at A. VB < VA Electric field lines always point in the direction of decreasing electric potential.

21. Ch 25.2 – Potential Difference in a Uniform E-Field Now, pretend a charge q0 moves from A to B. The change in the charge-field PE is: If q0 is a positive charge, then ΔU is negative. When a positive charge moves down field, the charge-field system loses potential energy.

22. Ch 25.2 – Potential Difference in a Uniform E-Field Electric fields accelerate charges… that’s what they do. What we’re saying here is that as the E-field accelerates a positive charge, the charge-field system picks up kinetic energy. At the same time, the charge-field system loses an equal amount of potential energy. Why? Because in an isolated system without friction, mechanical energy must always be conserved.

23. Ch 25.2 – Potential Difference in a Uniform E-Field If q0 is negative then ΔU is positive as it moves from A to B. When a negative charge moves down field, the charge-field system gains potential energy. If a negative charge is released from rest in an electric field, it will accelerate against the field.

24. Ch 25.2 – Potential Difference in a Uniform E-Field Consider a more general case. Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.

25. Ch 25.2 – Potential Difference in a Uniform E-Field Consider a more general case. Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.

26. Ch 25.2 – Potential Difference in a Uniform E-Field If sis perpendicular to E (path C-B), the electric potential does not change. Any surface oriented perpendicular to the electric field is thus called a surface of equipotential, or an equipotential surface.

27. Quick Quiz 25.2 The labeled points are on a series of equipotential surfaces associated with an electric field. Rank (from greatest to least) the work done by the electric field on a positive charge that moves from A to B, from B to C, from C to D, and from D to E.

28. EG 25.1 – E-field between to plates of charge A battery has a specified potential difference ΔV between its terminals and establishes that potential difference between conductors attached to the terminals. This is what batteries do. A 12-V battery is connected between two plates as shown. The separation distance is d = 0.30 cm, and we assume the E-field between the plates is uniform. Find the magnitude of the E-field between the plates.

29. EG 25.1 – Proton in a Uniform E-field A proton is released from rest at A in a uniform E-field of magnitude 8.0 x 104 V/m. The proton displaces through 0.50 m to point B, in the same direction as the E-field. Find the speed of the proton after completing the 0.50 m displacement.