Phys. 122: Tuesday, 10 Nov. HW 8 returned: please pick up yours in front. Written HW 11: due Thursday. Mast. Phys.: due in one week. Reading: Finish ch. 33 by Thursday. (You may skip/skim section 33.10: we won't cover LR circuits.) Exam 2: test corrections and/or bonus problem due by Thurs. (along with your original exam!). Bonus prob. is on our webpage and on Canvas. Clicker registrations: Please check your to see whether your registration didn't go through (and how to fix it). Class disruption: please keep voices down for the benefit of your classmates (Thursday was getting rather loud)!

Eligible for “test corrections”: #1 (i) - IF you missed more than 0.2 pts. #3 - IF you missed more than 0.2 pts. #7 [both parts (i) and (ii)]. [For (ii), note that I only wanted the E field due to the background V, not due to the charge mentioned in part (I).] #8 (= second “6,” on last page) is NOT eligible – answer was given Thursday. Bring corrections to OSL tutors; return them to me with your original test by Thurs. (Bring bonus problems straight to me.)

Magnetic Force on Charged Particles (chapter 32, section 7) Units of magnetic field (B) are Tesla (T). Force is at right angles to the velocity and at right angles to the magnetic field.

Motion perpendicular to a uniform B field is circular:

The full motion generally forms a helix:

Currents are charges in motion! So, currents can also feel the magnetic force. (Actually, this is only true for a straight wire. For curved wires, the correct expression is an integral (sum) of the force on each bit of the wire.) NEARLY ALL ELECTRICAL DEVICES WHICH PRODUCE MOTION FROM ELECTRICAL POWER RELY ON THIS FORCE RULE!

Example: “Rail Gun”

Conductors in equilibrium have a vanishing force per charge. In magnetic fields, this modifies the “electrostatics” rule for inside conductors that E = 0: A sneak peek ahead: this rule is at the basis of electromagnetic induction, which is where EMF that isn't from batteries originates.

Magnetic field sources: the same things which feel magnetic fields also cause them! (Charged particles in motion also do the trick. Substitute q v for I dL below for the charged particle version of Biot-Savart.)

The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law: Slide The Source of the Magnetic Field: Moving Charges

What is the direction of the magnetic field at the position of the dot? Slide QuickCheck 32.5 A. Into the screen. B. Out of the screen. C. Up. D. Down. E. Left.

The constant  0 in the Biot-Savart law is called the permeability constant:  0 = 4  × T m/A = × T m/A The SI unit of magnetic field strength is the tesla, abbreviated as T: 1 tesla = 1 T = 1 N/A m Slide The Magnetic Field

The magnetic field is revealed by the pattern of iron filings around a current-carrying wire. Slide Electric Current Causes a Magnetic Field

Another “right-hand rule”: this one is a shortcut for finding the direction of the B field created by a current. Treat B field lines as you do E lines: they point along the direction of the little (straight) vectors of the field. Density (closeness) of field lines gives the length of the field vectors.

Clickers: Two parallel wires carrying currents in the same direction will... a) Attract b) Repel c) Feel no net force d) Cause sparks to fly e) Rotate until they are perpendicular

Clicker Question 3 A flexible wire is wound into a flat spiral as shown in the figure. If a current flows in the direction shown, will the coil tighten or loosen? A.The coil will tighten. B.The coil will loosen.

Handy way to remember the new rules... Changing electric field rules to magnetic ones: 1) change E to B 2) replace ε ₀ by 1/ μ ₀ 3) replace q... by q (v x... )

Example: B at the center of a loop of current

Clickers: If you multiply (Farads/meter) by (Tesla meters/ Ampere), what units do you get? a) Watts b) Seconds c) Coulombs d) Squared Newtons (like Fig Newtons) e) seconds squared/(meters squared)

Shortcuts for finding B: the analogous version of Gauss' Law isn't too helpful...

Clickers: what does the magnetic version of Gauss' Law tell us? a) Magnetic field surfaces never enclose any charge b) Magnetic field loops never enclose any current c) Magnetic field lines always end on negative charge d) Magnetic field lines can't begin nor end e) Closed surfaces are impossible to draw in magnetic fields

Ampere's Law: the actual “shortcut” for finding the B field when things are very symmetrical. (The “long way” is Biot-Savart.) There are only a few situations which are symmetric enough: the long straight wire, solenoids (wire coils), and infinite sheets of current are most of them.