1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lectures 24-25

2. The Magnetic Field

5. The force on a charge q moving with a velocity
The magnitude of the force

6. left-hand rule
right-hand rule

7. Motion in magnetic field
1) Uniform ,
2) Uniform ,
3) Nonuniform

9. The angular velocity

10. The angular velocity (cyclotron frequency )
does not depend on velocity!
The force is always perpendicular to velocity, so it cannot change the magnitude of the velocity, only its direction.
The work done by the magnetic force is zero!
Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed.

11. Gauss’s Law
The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by

12. Conductors and insulators
Charges reside at the surface of the conductor + + + + + + + +
Conductor + +
E=0 + + + + +

13. Electric field of a ball of chargeQ
Electric field outside of a charged sphere is exactly the same as the electric field produced by a point charge, located at the center of the sphere, with charge equal to the total charge on the sphere.

14. Insulating sphere with charge Q uniformly spread throughout the volume

15. Conducting sphere with charge QV r A r

16. A Charged, Thin Sheet of Insulating Material+ + + + + + + + + + +

17. A field in a cavity of a conductor Faraday’s cage

18. Electric field near a surface of a conductor

19. Spherical capacitor; Cylindrical capacitor
The capacitance is:
Spherical capacitor; Cylindrical capacitor

20. If the capacitors were initially uncharged,
Capacitors in series:
Capacitors in parallel:

21. Current Density for j =Const only!
Consider current flowing in a homogeneous wire with cross sectional area A.
for j =Const only!

22. Current, Ohm’s Law, Etc.

23. For steady state situation
Kirchhoff’s junction rule: The algebraic sum of the currents into any junction is zero.
Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop must be zero.

24. Joule’s Law

25. Resistors in series:
Resistors in parallel:

30. >90
>80
>70
>60
>50
>40
<40
Average 57.7