Ch29 - Physics 4B Lecture Notes Chapter 29 - Magnetic...

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Physics 4B Lecture Notes 29-1 Chapter 29 - Magnetic Fields Problem Set #8 - due: Ch 29 - 2, 5, 12, 14, 21, 30, 34, 37, 41, 45, 46, 49, 55, 60, 64, 69 It turns out the hardest thing to understand about magnetism is a simple magnet. We will start by studying the force on a current caused by a magnet field. We'll wait until next chapter to figure out where the magnetic field comes from. Lecture Outline 1. The Force Between Currents 2. The Definition of the Magnetic Field 3. The Magnetic Force on a Moving Charge 4. Current Loops in a Constant Field 5. Magnetic Devices 1. The Force Between Currents Current Balance There are similarities between the electric force and the force between wires. I 2 1 I q 1 F 12 q 2 21 F 21 F F 12 Could the force between wires just be the electric force? It would appear not because: 1)Like currents attract and opposite repel, exactly the reverse of the electric force. 2)The current carrying wires are electrically neutral. They exert no force on a single charge. It would seem that we must treat the force between current carrying wires as a new force called the "magnetic force." It must be noted that, in fact, this force is electrical in nature and Einstein's Theory of Relativity explains the connection between electricity and magnetism. We need to establish the force law (analogous to Coulomb's Rule or Newton's Law of Universal Gravitation) for this "new" force of magnetism. Newton's Third Law requires F 12 = F 21 Guess: F 12 I 1 , F 12 I 2 , F 12 1 r and F 12 l . F m = μ o 2 π I 1 I 2 r l The Force Between Current Carrying Wires where the constant μ o 4 π x10 - 7 N A 2 . I 2 1 I F 12 21 F l r
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Physics 4B Lecture Notes 29-2 2. The Definition of the Magnetic Field Recall the way we defined the electric field. Instead of thinking of q 1 exerting the force on q 2 , we think of q 1 creating a field and the field exerting the force on q 2 . r 1 q q 2 21 F q 2 21 F E 1 where F 21 = q 2 E 1 . We can do the same thing with the magnetic field, B. I 2 1 I F 12 21 F l r I 2 21 F l B 1 where F 21 = I 2 l B 1 . To incorporate the vector nature of forces we need to pick a direction for the magnetic field. Since r F is up and r l is in the horizontal plane along the wire, it is most convenient to choose r B into the paper. Now we can define the magnetic field vector, r F I r l × r B The Definition of the Magnetic Field Note the units: F [ ] = I [ ] l [ ] B [ ] ⇒ B [ ] = F [ ] I [ ] l [ ] = N A m It is convenient to define a new unit 1 N A m 1 Tesla = 1T. A second common unit is 1 Gauss = 1G = 10 - 4 T. Currents are the source of the magnetic field. We will discuss this in detail in the next chapter. This chapter will focus on the effect of an applied magnetic field.
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Ch29 - Physics 4B Lecture Notes Chapter 29 - Magnetic...

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