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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

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

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

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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

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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

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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

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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

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

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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

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10 Magnetic Field of a Circular Current Loop Figure 28-12 B y = 0

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11 Magnetic Field of a Circular Current Loop (on the axis of N circular loops)(x=0) Figure 28-13 x Figure 28-14

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

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

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

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15 Ampere’s Law Figure 28-16

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16 Applications of Ampere’s Law Example 28-9 Field of a Solenoid (magnetic field is concentrated in side the coil) Figure 28-20 Figure 28-21 n = turns/meter where N = total coil turns l = total coil length turns/meter (28-23)

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17 Applications of Ampere’s Law Example 28-9Field of a Solenoid Figure 28-22 where N = total coil turns l = 4a = total coil length turns/meter

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18 Applications of Ampere’s Law Example 28-10 Field of a Toroidal Solenoid – (field is inside the toroid) Figure 28-23 Path 1 Path 3 Path 2 N turns (28-24) Current cancels No current enclosed

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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

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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

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