1. Magnetic fields are force fields that exert non-contact forces on other magnets or current-carrying conductors. They are generated by moving charges and currents. 2. Magnetic field lines emanate from the north pole of a magnet and loop back to the south pole. Opposite magnetic poles attract, while like poles repel one another. 3. A magnetic force is exerted on any moving charge or current in a magnetic field. This force is perpendicular to both the magnetic field and the velocity of the charge or current.

1. Magnetic Field Sources

2. Magnetic Fields A force field that denotes the area in which the non-contact force of permanent magnets or current carrying conductors can exert their influence Fields are concentrated at the poles Same properties with Electric field lines except that there is no magnetic monopole

3. Magnetic field lines

4. Magnetic Force Like poles repel, opposite attract An object that contains iron but is not itself magnetized is attracted by either pole of a permanent magnet.

5. Magnetic Force

6. Magnetic interactions can be described as: A moving charge or a current creates a magnetic field in the surrounding space (in addition to its electric field) The magnetic field exerts a force F m on any other moving charge or current that is present in the field. The magnetic force F m acting on a positive charge q moving with velocity v is perpendicular to both F m and the magnetic field B.

7. Units of Magnetic Fields SI units: tesla , T 1 tesla = 1 T = 1 N/A · m Or: gauss , G 1 G = 10 -4 T

8. Magnetic Force on Moving Charge Moving charged particles are deflected in magnetic fields Right-Hand Rule

9. Grip and Hand Rules Out of the Page In to the Page

11. Magnetic Force on Moving Charge The magnetic force is always perpendicular to v ; a particle moving under the action of a magnetic field alone moves with a constant speed.

12. Motion of charged particles in a magnetic field

13. Motion of charged particles in a magnetic field Fig. 27.18

14. Motion of charged particles in a magnetic field Fig. 27.17

15. Applications of motion of charged particles Velocity Selector Particles of a specific speed can be selected from the beam using an arrangement of electric and magnetic fields called a velocity selector.

16. Magnetic Force on Current Carrying Wire

17. Magnetic Force on Current Carrying Wire

18. Ampere’s Law Used to determine the magnetic field yielded by current-carrying wire Ampere’s law states that the product B and length of line segment around any closed path equals µ 0 times the net current through the area enclosed by the path. Direction of Magnetic field is determined by corkscrew method

19. Ampere’s Law B=  0 I/2  L

20. Magnetic field profile of 2 parallel current carrying wires

21. Solution

22. Magnetic Field in Solenoid

23. Magnetic Field in Solenoid B=  0 nI

24. Ampere’s Experiment B 1 =  0 I 1 /2  L F=  0 I 1 I 2 l/2  L

25. Exercise B 1 =  0 I 1 /2  L F/l=  0 I 1 I 2 /2  L

26. Example Suspending a current with a current A horizontal wire carries a current I 1 =80 A dc. A second parallel wire 20 cm below it must carry how much current I 2 so that it doesn’t fall due to gravity? The lower wire is a homogenous wire with a mass of 0.12 g per meter of length. F/L = mg/L =1.18 x 10 -3 N/m  0 I 1 I 2 /2  L = 1.18 x 10 -3 N/m I 2 = 15 A

27. Definitions Ampere current flowing in each of the two long parallel conductors 1 m apart, which results in a force of exactly 2 x 10 -7 N/m of length of each conductor. Coulomb one ampere-second

28. Solution Set F/l=  0 I 1 I 2 /2  L F A /l= 5.83 x 10 -5 N/m; 90 F B /l=3.37 x 10 -5 N/m; -60 F C /l=3.37 x 10 -5 N/m; 240