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 webpageand on Canvas. Clicker registrations: Please check your email 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), notethat I only wanted the E field due to thebackground V, not due to the chargementioned in part (I).]#8 (= second “6,” on last page) is NOTeligible – answer was given Thursday.Bring corrections to OSL tutors; return themto me with your original test by Thurs. (Bringbonus 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 andat right angles to the magnetic field.

Motion perpendicular to a uniform B fieldis circular:

The full motion generally forms a helix:

Currents are charges in motion! So, currentscan also feel the magnetic force.

(Actually, this is only true for a straight wire.For curved wires, the correct expression isan integral (sum) of the force on each bit of thewire.)

NEARLY ALL ELECTRICAL DEVICESWHICH PRODUCE MOTION FROMELECTRICAL POWER RELY ON THISFORCE RULE!

Example: “Rail Gun”

Conductors in equilibrium have a vanishingforce per charge. In magnetic fields, thismodifies the “electrostatics” rule for insideconductors that E = 0:

A sneak peek ahead: this rule is at the basisof electromagnetic induction, which iswhere EMF that isn't from batteriesoriginates.

Magnetic field sources: the same thingswhich 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 32-44

The Source of the Magnetic Field: Moving Charges

What is the direction of the magnetic field at the position of the dot?

Slide 32-54

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 × 10-7 T m/A = 1.257 × 10-6 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 32-45

The Magnetic Field

The magnetic field is revealed by the pattern of iron filings around a current-carrying wire.

Slide 32-35

Electric Current Causes a Magnetic Field

Another “right-hand rule”: this one is a shortcutfor finding the direction of the B field createdby a current.

Treat B field lines as you do E lines: they point alongthe direction of the little (straight) vectors of the field.Density (closeness) of field lines gives the length ofthe 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 ε₀ by 1/μ₀

3) replace q ... by q (v x ... )

Example: B at the center of a loop ofcurrent

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 analogousversion of Gauss' Law isn't too helpful...

Clickers: what does the magnetic versionof 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” forfinding the B field when things are verysymmetrical. (The “long way” is Biot-Savart.)

There are only a few situations which aresymmetric enough: the long straight wire,solenoids (wire coils), and infinite sheetsof current are most of them.