1. Magnetic Forces and Fields

2. Magnetic Force

3. Right Hand Rule: Cross Product

4. Magnetic Force on a Wire

5. F B and Circular Motion

6. Velocity Selector Only charges with the proper velocity will pass through undeflected.

7. Mass Spectrometer Particles are ionized and sent through velocity selector. Radius depends on mass if charge and velocity are equal.

8. The Cyclotron

9. Torque on a Loop Define a unit vector perpendicular to the plane of the loop.

10. Torque on a Loop For each side of length a: No force is produced on sides of length b since current is parallel to B. Net force on loop is zero but torque will be produced due to forces on the other sides. Calculating torques about the midpoint of the loop, Since there are two sides:

11. The Hall Effect Current through conducting strip causes charge separation and establishes potential difference due to magnetic force on moving charges. If mobile charges are positive, top of strip is positive due to upward force.

12. The Hall Effect If mobile charges are negative, force is still upward by top of strip will be negative, allowing for identification of mobile charge type. If potential difference is measured, magnetic field strength or drift velocity can be calculated.

13. Field of a Bar Magnet

14. Biot-Savart Law Similar to Coulomb’s Law for electrostatics Define differential current element Ids Integrate over current distribution to find total magnetic field

21. Ampere’s Law With the proper symmetry, Ampere’s Law can be used in place of Biot-Savart Similar to Gauss’ Law for electrostatics B must be constant along the path of integration and parallel to the differential of length, dl