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Currents cause magnetic fields. If we say that the compass lines up along the field, then the field curls around the wire. B field lines have no beginning or end! Permanent magnets are just collections of little current loops In Jules Verne’s story “Journey to the Center of the Earth”, some dudes travel deep inside the Earth. If this were possible and they had a compass with them, what direction would their N compass needle point? A] toward the Earth’s northern geographic pole B] toward the Earth’s southern geographic pole C] it would have no preferred direction Magnetic field lines curl around currents, forming closed loops. As such, they have no beginning and no end. • What is the total flux of the magnetic field through any closed surface? Recall that E dA q enc B dA ? A] 0 B] Ienc times a positive constant C] -Ienc times a positive constant /0 Note key differences with E fields: NO force if v=0 NO force if v is parallel to B Direction of force depends on direction of v (perp to v!) What is the magnitude of the magnetic force on the charge moving with velocity v3? What is the magnitude of the magnetic force on the charge moving with velocity v1? What is the magnitude of the magnetic force on the charge moving with velocity v2? What is the direction of the magnetic force on the charge moving with velocity v2? Centripetal force = Fmag Cyclotron frequency Part a. Use A for i), B for ii) etc. Radius is proportional to v. Ans. B (ii) Part b. Use A for i), B for ii) etc. Because r is proportional to v, the period is unchanged. Ans. A (i) velocity Use A for i), B for ii) etc. Same speed. Ans C (iii) F I l B wire F qv B charge http://www.falstad.com/vector3dm/ Why do compass needles align with B? Why do opposite poles attract? Why do magnets attract iron? The electric potential is A] higher at A B] higher at B C] the same in both places If the current direction were the same, but electrons carried the current, where would the electric potential be higher? B The unit of the magnetic field B (the Tesla) A] is the same as the electric field times a velocity B] is the same as the electric field divided by a velocity C] cannot be expressed as either of these (The electric field is V/m.) What is the sign of the charge carriers in this conductor? A] + B] C] Can’t tell What is the drift velocity of the negative charge carriers? A] 0 B] 10-3 m/s C] 10-2 m/s D] 10-1 m/s E] 1 m/s 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 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 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 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 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! This “version” of the right hand rule gives the same result as v ˆ Try it. dl r What is the contribution of the straight sections of the wire to the magnetic field in the center of the semicircle? A] Each contributes 0 B] They both have contributions that are opposite, and so add to 0 C] Each contributes 0 I 2R D] infinite 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 0 I B] 2x 0 I C] x D] Insufficient information B=0 iii Currents out of plane attractive 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” B dl I 0 B 0 J E 0 B dA 0 B 0 E / 0 These are what we (in physics 161) know now. They are still incomplete: we will fix them in the remaining weeks. Maxwell’s Equations (corrected) E B 0 J 00 t B E t B 0 E / 0 Nothing would demonstrate your love of, and dedication to physics like a…. Maxwell Equations Tattoo ! B 0 J 00 E E t B t B 0 E / 0 And… they look great on chicks as well as dudes…