1. Lecture 15-1 What we learned from last class Define magnetic dipole moment by where n is normal to the loop with RHR along I. Hall effect:  Determines the sign and number of carriers.  Measures B.

2. Lecture 15-2 Van Allen belts

3. Lecture 15-3 Sources of Magnetic Fields Permeability constant Moving point charge: Bits of current: I Biot-Savart Law The magnetic field “circulates” around the wire.

4. Lecture 15-4 Magnetic field due to a current loop Principle of superposition: At the center, On axis generally,

5. Lecture 15-5 Circular Loop Current as a Magnetic Dipole

6. Lecture 15-6 Magnetic Field of Circular Arc Current I runs clockwise in the closed loop wires below: What is B at center?

7. Lecture 15-7 PHYS241 – warm-up A circular current loop lies in the plane perpendicular to this sheet with its axis along the x-direction, and produces magnetic field B as shown. What is the direction of the current at the top end of this loop? a. Out of the sheet b. Into the sheet c. Along +x axis d. Along  x axis e. Current is zero. x

8. Lecture 15-8 Gauss’s Law for Magnetism sources No sources Gauss’s Law Gauss’s Law for Magnetism

9. Lecture 15-9 Magnetic field of a solenoid A constant magnetic field could be produced by an infinite sheet of current. In practice, however, it is easier and more convenient to use a solenoid. A solenoid is defined by a current I flowing through a wire that is wrapped n turns per unit length on a cylinder of radius R and length L. L R

10. Lecture 15-10 Magnetic field of a solenoid (continued) Contribution to B at origin from length dx one turn # turns in length dx (or for L>>R) (half at ends)

11. Lecture 15-11 Solenoid’s B field synopsis // to axis Long solenoid (R<<L): B inside solenoid B outside solenoid nearly zero (not very close to the ends or wires)

12. Lecture 15-12 RHIC STAR Experiment STAR

13. Lecture 15-13 Magnetic field of a Straight Current I y Infinite straight current http://falstad.com/vector3dm/

14. Lecture 15-14 Two Perpendicular Currents I1I1 I2I2 F B 1,2 F B 1,3 I3I3 B B F B2,1

15. Lecture 15-15 PHYS241 - Quiz A A circular current loop lies on the xy-plane as shown, where the current is clockwise as seen from the positive z-axis. What is the direction of the B field at point A? a. Along +x axis b. Along +y axis c. Along +z axis d. Along  z axis e. Along  x axis z x y A I

16. Lecture 15-16 PHYS241 - Quiz B A circular current loop lies on the xy-plane as shown, where the current is clockwise as seen from the positive z- axis. What is the direction of the B field at point A? a. Along +x axis b. Along +y axis c. Along +z axis d. Along  z axis e. Along  x axis z x y A I

17. Lecture 15-17 PHYS241 - Quiz C A circular current loop lies on the xy-plane as shown, where the current is clockwise as seen from the positive z- axis. What is the direction of the B field at point A? a. Along +x axis b. Along +y axis c. Along +z axis d. Along  z axis e. Along  x axis z x y A I