2. Magnetic Field Lines Graphical Illustration of Magnetic Fields Lines start on north pole and end on south pole Opposite poles attract, like poles reply Density of lines tells strength of field. Key differences between magnetic fields and electric fields: All magnets have a north and south pole! No such thing as an isolated north or south pole. (have magnetic dipoles, not monopoles) Different force laws!

4. Motion of a charged particle in a uniform B- field:Perpendicular v charge q F F R

5. Motion of a charged particle in a uniform B-field: Parallel v charge q Which way will it accelerate now? A)RightC) B) LeftD) no acceleration Motion along the magnetic field will be at uniform speed Most general motion is a helix

6. General Motion of a charged particle in a uniform B-field Suppose the charge moves at an angle; neither parallel nor perpendicular The velocity has two components then: parallel and perpendicular The perpendicular component causes circular motion The parallel component is unaffected by the magnetic field The overall motion is a superposition of circular and uniform: a helix!

7. Force on a wire charges q i Magnetic Field B Length L Length vector in direction current is flowing

8. Force on a wire Magnetic field or wire may not be constant I

9. Quiz

10. Torque on a Loop: Simple Magnetic Field B I I Force on top and bottom is zero There is a net torque on the loop Force on right side is into the plane Force on left side is out of the plane a b

11. Torque on a Loop: Rules Define the area vector of a loop as a vector of length A perpendicular to the loop The direction of the vector is determined by right-hand-rule based on current direction I I Direction of torque can be worked out using cross-product Magnitude of torque as well Torque causes the loop to rotate so that the normal vector is parallel to the field

12. Torque on a Loop What is the torque on the wire? A)4  10 -2 N  mD)  10 -4 N  m B)  10 -2 N  m C)4  10 -4 N  m B = 1 T 2 cm Which direction does the torque twist the loop? A)Right towards, left away B)Right away, left towards C)Top towards, bottom away D)Bottom towards, top away I = 1A

13. Potential Energy of a Loop When you rotate a loop in a magnetic field, the loop is doing work Since it is doing work, the energy is changing Integrate to get potential energy Loop likes to align itself with magnetic field

14. Multiloops If there are N loops basically all identical, multiply by N All the properties of the wire are summarized in the magnetic dipole moment of the wire Units of A  m 2 = J/T