Sources of Magnetic Field Chapter 28 Study the magnetic field generated by a moving charge Consider magnetic field of a current-carrying conductor Examine the magnetic field of a long, straight, current-carrying conductor Study the magnetic force between current- carrying conductors Consider the magnetic field of a current loop Examine and use Ampere’s Law 1

The magnetic field of a moving charge A moving charge will generate a magnetic field relative to the velocity of the charge. 2

3 Magnetic Field of a Moving Charge) (28-1) Permeability of free space Direction of B determined by Magnitude of B The vector form :

Force between two moving protons Two protons moving at the same velocity (much less than speed of light) in opposite directions. The electric force F E is repulsive. The right-hand rule indicates the magnetic force F M is repulsive. (i x k=-j) Find the ratio of the magnitude of the forces. The ratio of the two forces. Where c=speed of light. Therefore: F E >>F B

5 Magnetic Field of a Current Element Figure 28-3 Let dQ = charge in wire segment dl Let A = cross section area of wire segment dl Let n = charge density in wire segment dl dQ = nqAdl I = nqv d A (28-5)Biot-Savart Law Direction of dB determined by Vector form of Biot-Savart Law Total magnetic field of several moving charges = vector sum of fields caused by individual charges

Magnetic field of a straight current-carrying conductor Biot and Savart contributed to finding the magnetic field produced by a single current-carrying conductor. 6

7 Magnetic Field of a Current-Carrying Conductor Figure 28-5 If a  x Based upon symmetry around the y-axis the field will be a circle

8 Magnetic Field of a Current-Carrying Conductor Figure 28-6 where r = perpendicular distance from the current-carrying wire.

9 Force between Parallel Conductors Each conductor lies in the field set up by the other conductor Note: If I and I’ are in the same direction, the wires attract. If I and I’ are in opposite directions, the wires repel. See Example 28.5 Page 966 Only field due to I shown Substitute for B

10 Magnetic Field of a Circular Current Loop Figure B y = 0

11 Magnetic Field of a Circular Current Loop (on the axis of N circular loops)(x=0) Figure x Figure 28-14

Ampere’s Law I—specific then general Similar to electric fields if symmetry exists it is easier to use Gauss’s law 12

Ampere’s Law II The line integral equals the total enclosed current The integral is the sum of the tangential B to line path

14 Ampere’s Law (Chapter 28, Sec 6) Figure For Figure 28-15a For Figure 28-15b For Figure 28-15c

15 Ampere’s Law Figure 28-16

16 Applications of Ampere’s Law Example 28-9 Field of a Solenoid (magnetic field is concentrated in side the coil) Figure Figure n = turns/meter where N = total coil turns l = total coil length turns/meter (28-23)

17 Applications of Ampere’s Law Example 28-9Field of a Solenoid Figure where N = total coil turns l = 4a = total coil length turns/meter

18 Applications of Ampere’s Law Example Field of a Toroidal Solenoid – (field is inside the toroid) Figure Path 1 Path 3 Path 2 N turns (28-24) Current cancels No current enclosed

Magnetic materials The Bohr magneton will determine how to classify material. Ferromagnetic – can be magnetized and retain magnetism Paramagnetic – will have a weak response to an external magnetic field and will not retain any magnetism Diamagnetic – shows a weak repulsion to an external magnetic field 19 Bohr Magneton- In atoms electron spin creates current a loop, which produce magnetic their own field

Ferromagnetism and Hysteresis loops The larger the loops the more energy that is lost magnetizing and de- magnetizing. Soft iron produce small loops and are used for transformers, electromagnets, motors, and generators Material that produces large loops are used for permanent magnet applications