Last time: Fields from Moving Charges & Current-carrying wires First, a correction of a slightly tricky sign error! (which will NOT be on the exam.) Potential energy associated with magnetic torque on a current loop.

Let’s use Biot-Savart to find the field at the center of a current loop. And an infinite wire.

Just like electric fields, magnetic fields obey the principle of (vector) superposition. The field from several sources is the vector sum of the fields from each source.

Point P is a perpendicular distance x from each wire Point P is a perpendicular distance x from each wire. Both wires carry current I in the direction shown. What is the magnetic field at P? A] 0 B] C] D] Insufficient information 4

Point P is a perpendicular distance x from each wire Point P is a perpendicular distance x from each wire. Both wires carry current I in the direction shown. What is the magnetic field at P? A] 0 B] C] D] Insufficient information 5

A proton (+) and an electron (-) move side by side both with velocity v as shown. What is the direction of the magnetic field at the electron due to the proton (in our “laboratory” frame of reference)? A] into page B] out of page C] upward D] downward E] to the right 6

A proton (+) and an electron (-) move side by side both with velocity v as shown. The magnetic field is into the page, by RHR. What is the direction of the magnetic force on the e- ? A] into page B] out of page C] upward D] to the left E] to the right 7

A proton (+) and an electron (-) move side by side both with velocity v as shown. The magnetic force on the electron is away from the proton. What direction is the total (electric + magnetic) force on the electron? (v<c) A] into page B] out of page C] upward D] to the left E] to the right 8

What is the total force on the electron if v=c? A] 0 A proton (+) and an electron (-) move side by side both with velocity v as shown. The total force on the electron is still attractive, but weaker than if no magnetic force were present. What is the total force on the electron if v=c? A] 0 B] infinite, away from the proton C] infinite, toward the proton 9

What is the total force on the electron if v=c? Ans 0! A proton (+) and an electron (-) move side by side both with velocity v as shown. The total force on the electron is still attractive, but weaker than if no magnetic force were present. What is the total force on the electron if v=c? Ans 0! Clocks slow to a STOP as v -> c! 10

Be sure you can do the clicker quizzes, especially the circuit we did in class. I'm going to change the numbers and give you the same problem.Also, go over the worksheets (posted) that we did in 168, the problems class. Be sure you can answer questions correctly about how circuits behave if a lightbulb is removed. Also, understand the behavior of a 60 W and 100 W light bulb in series, and in parallel. Make sure you can use the right hand rule and cross product (in the form of vBsin theta) to find magnetic force, and also to find magnetic fields. Focus on the concepts, I am trying to avoid all but the simplest computations on the exam. (Asking questions like what happens to B field if you double the distance to a charge does not count, IMO, as a complicated computation.) An example of finding B where you need components. Ampere’s law Solenoids

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A= i B= ii, etc. 13

A= i B= ii, etc. 14

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A= i B= ii, etc. 16

In Ampere’s law, Gauss’ law, etc. : If we let loops and surfaces get infinitesimally small, we get relationships for derivatives of the fields. There are four relationships, called “Maxwell’s Equations” These are what we (in physics 161) know now. They are still incomplete: we will fix them in the remaining weeks. 17

Maxwell’s Equations (corrected) Nothing would demonstrate your love of, and dedication to physics like a…. Maxwell Equations Tattoo ! 18

Very sexy for gals as well as guys! 19