Welcome to Physics 7C! Lecture 6 -- Winter Quarter Professor Robin Erbacher 343 Phy/Geo

Announcements Course policy and regrade forms on the web: If you received rubric code 4 on part b) of Quiz 2, please hand in your quiz for a possible regrade. Quiz today on Block 13, DLMs 9 and 10. Block 13 continues: DLMs 11 and 12 this week. 3 DLs canceled on Thursday: 10:30, 4:40, 7:10. Turn off cell phones and pagers during lecture.

Gradients: Potential Energy Recall: What is the potential energy of a mass m in a the Earth’s gravitational field, a height h above the surface of the Earth? PE = mgh ! Force on a mass m in gravity field g is F = mg. Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass: The direction of the force on the mass m is toward decreasing PE grav (hence the negative sign!) Gradient relation

Gradients for E Fields: Potential Analogous to the gravitation case: Force on a charge q in an Electric field E is F = qE. Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass: The direction of the force on the charge +/- q is toward decreasing PE grav (hence the negative sign again!)

Electric Potential V Electric potential V depends on position, and distances. The electric field E can be determined by the spatial derivative of an electric potential, V. PE = qV +- E +q What is the change in potential energy if the charge +q moves from the positive plate to the negative plate? We need more information: distance between the plates, voltage drop across the capacitor, …

Magnetic Fields and Forces Analogy to Gravity/Electric fields: Magnetic Fields We can think about moving charge I (current) exerting a force on a moving charge qv. Object A Object B exerts force Direct Model of Forces field Object B exerts force Object A field creates Field Model of Forces

Magnetic Field B We have now derived the magnetic field B, which exists in the presence of moving charge (or current) I : What does B depend on?What units does it have? In which direction does it point? Magnitude of magnetic field: 1/r …and current I Teslas

Electric and Magnetic Field Maps

Force due to B Field The force on a moving charge due to a B field is: What direction is the resulting force? (What is this cross-product thing?) The Hall Effect (1897)

Electrons as Particles We know that moving electric charges cause magnetic fields. Another source of magnetism can be “spin”. Electrons orbiting nuclei create current loops Protons and electrons themselves have rotation: Spin! The electron is a source of both an electric field (due to its negative charge) and a magnetic field (due to its "spin") EB e ﾐ e ﾐ e- 1s 2s 2p 3s 3p 4s 3d Hund's Rules for Fe Hund’s Rules for electron shells levels: Electrons pair up and cancel out magnetic Properties. Leftover electrons can give More magnetic properties, like with Fe 2+.

Harmonic Waves and Light Electric and magnetic fields are everywhere surrounding charges. If we send them into simple harmonic motion, the fields fluctuate in a spatially and time-varying way.  This is light! An electromagnetic (EM) wave! E(z) at a particulart x � y � z � y

Alternating Currents (AC) As you see in DLM 11, you induce a current by moving a loop through a B field. The current acts to oppose a change in B field through the loop.  Lens’ Law! The current changes direction as you move in and out. Our regular household power is 110V AC. (Can get 220V, multi-phasic, etc). What does DC mean?