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There will be a quiz next Tuesday, April 14 From now until the end of the semester, we will have 2 problem solving session per week. Next week, we will have one on Monday, April 13 at 1:00 PM and one on Thursday, April 16 at 1:00 PM. The electron spins on its axis, giving rise to a electron current in the direction of rotation. Think of the electron as a ball with charge distributed over its surface. When the ball spins, that charge is set in motion around the electron's spin axis, resulting in a magnetic field specific to the electron. The electron is like a magnetic dipole, a miniature magnet, with a north end and a south end. In most substances, electrons spin in random directions - magnetic fields cancel. For iron and other magnetic substances, the spin magnetism is not canceled. Can be permanently magnetized by placing in strong magnetic field and permanently aligning atoms - can be demagnetized by dropping magnet and jostling atoms out of alignment. Electromagnetic produced by wrapping coil around iron bar - magnetic field produced that aligns atoms in bar - more coils or more current - larger magnetic field and greater atomic alignment Magnetic Dipoles and How Magnets Work The Direct-Current Motor Magnetic Field of a Moving Charge 0 qv sin B 4 r 2 B 0 q v r 4 r 2 Magnetic field of a point charge moving with constant velocity 1 1 0 T m / A ; 4 c 0 7 00 2 Example: Force between two moving protons Find the ratio of electric and magnetic forces on the protons 1 q2 F E 4 0 r2 0 qv B k 2 4 r Magnetic field of the lower proton at the position of the top one F qv ( )B B 4 r 22 q 0 v F j B 2 2 F 2 v B v 2 00 F c E Magnetic Field of Current Element The Biot-Savart law. d Q n q A d l f l o w w i t h v e l o c i t y v d For element of a (fine) wire: I dl rˆ dB 0 4 r 2 constant permeability of free space: For the whole "circuit": 0 I dl rˆ B 4 r 2 For arbitrary distribution of charge flow: j(1) rˆ12 B(2) 0 dV1 2 4 r12 (rˆ12 is from point 1 to point 2) Magnetic field around a straight wire For the fieldmagnitude : 0I sin dx B 2 4 r a ad [r ; x acot; dx 2 ] sin sin 0I 0I sin d 4a 0 2a (where ais thedistance fromthewire) Magnetic Field of Two Wires Field at points on the x-axis to the right of point (3) I 0 B ; 1 2 ( xd ) I 0 B ; 2 2 ( xd ) I d 0 B B B t o t a l 2 1 2 2 ( x d) Magnetic field outside of a conductor pair falls off more rapidly Magnetic field of a circular arc For the field magnitude at O : 0 I B 4R 2 0 I ds 4R 2 R 0 I 4R