Electric Fields and Capacitors

1. Electric Fields and Capacitors The basis of Electric storage

2. A Learning Summary • Two objects are just resolved when the central diffraction maximum of one object is at the first minimum of the other. (Rayleigh’s criterion) • As before, q is approximately tan q = y/L • Circular aperture has diameter d

3. What type of forces could act on e-? Gravity, if . . . • another mass is around. Electricity, if . . . • another charged object is around. Magnetism, if . . . • the e- is in a magnetic field The weak nuclear force, if . . . • any other fermion is around

4. Gravity’s force between e- and p+ Force between two objects due to gravity: m1 = me = 9.11 E-31 kg m2 = mproton = 1.67 E-27 kg r = 1 nm = 10-9 m F = 1.01 E-49 N

5. Electrical force between e- and p+ Force between two objects due to Coulomb (electric) attraction: q1 = qe = 1.602 E-19 C q2 = qproton = 1.602 E-19 C r = 1 nm = 10-9 m F = 2.31 E-10 N

6. Nuclear force between e- and p+ Force between two objects due to the weak nuclear force: s = 2mc2E = 1 GeV2 = 2.5 E-20 J2 mW = 1.42 E-25 kg r = 1 nm = 10-9 m GF = 4.52 E 14 J-2 F < 1 E -100,000 N

7. Comparing forces between e- and p+ Electric: F= 2.31 E-10 N Gravity: F= 1.01 E-49 N Nuclear: F < 1 E -100,000 N If I had 1% more electrons than protons, and I stood an arm’s length away from a similarly imbalanced person, the force between us would be great enough to lift a weight the size of . . . • The earth!

8. How can a force act at a distance? If I took my electron away from the proton and brought a positron (positive e) near the proton, the positron would . . . • accelerate away from the proton So, does my proton exert a force if no one is around to feel it? • Force, no. But we can define an electric field which describes the force a charge would feel if it came near the proton

9. How can a force act at a distance? A charge creates an electric field that fills space, whether or not any other charge is around to feel its effects!

10. Make Predictions for the Activity, then Answer Questions 1-7 of the Activity

11. What’s a Field? Electric field E = F/q, where q is the charge feeling the force Since forces obey the law of linear superposition (i.e., they add), electric fields add too!

12. What does a “field” look like?

13. Finish the Activity, working as far as you can in the time allowed

14. Charges in Conductors • Electric fields are created when positive charges and negative charges are separated • A uniform electric field existing over a region sets up a potential difference between points in that region: DV=EDx, where Dx is the distance along a field line. • If I apply a potential difference across a conducting object (including semi-conductors), charges experience a force, and charge carriers will flow until the potential difference is removed.

15. What if charge can’t flow? • Consider charge separated by two metal plates • A potential difference exists between the plates • An electric field exists between the plates, pointing from positive plate to negative plate • No current can flow

16. Introducing, . . . The Capacitor

17. Introducing, . . . Capacitance The battery provides the work needed to move the charges and increase their potential energy

18. What determines capacitance? C = e0 A/d

19. More about capacitors

20. More about capacitors U = Vq = Ve 1 eV = 1.602 x 10-19 J = energy to move electron through 1 volt