Ch30 - Physics 4B Lecture Notes Chapter 30 Magnetic Fields...

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Physics 4B Lecture Notes 30-1 Chapter 30 - Magnetic Fields Due to Currents Problem Set #9 - due: Ch 30 - 3, 12, 17, 19, 26, 37, 38, 47, 51, 54, 57, 64, 72 Lecture Outline 1. The Biot-Savart Rule 2. Ampere's Law Now that we know the effects of magnetic fields on currents we can discuss the causes of magnetic fields. If currents feel the magnetic force, Newton's Third Law requires they must exert it as well. The purpose of this chapter is to learn to calculate magnetic fields caused by currents. The Biot-Savart Rule is a recipe that will always work. Ampere’s Law, while more fundamental, can be used to find fields only in cases where the current distribution is highly symmetric. 1. The Biot-Savart Rule r r I 2 1 I q 1 dq 2 + + r r s r d r E 2 = k dq 2 r 2 ˆ r d r s d r F 12 = q 1 d r E 2 d r F 12 = I 1 r s × d r B 2 The electric force on a charge q 1 is found from the field due to all the other charges. We begin by finding the field due to the point charge dq 2 , which is d r E 2 = k dq 2 r 2 ˆ r . Next, the force on q 1 due to dq 2 is found using definition of electric field, d r F 12 = q 1 d r E 2 . Then integrate all the contributions from the rest of the charge distribtion. The same proceedure would work for the magnetic force on I 1 due to a distribution of current I 2 . The magnetic force on the current I 1 in the magnetic field d r B 2 caused by a small current element in I 2 is, d r F 12 I 1 r s × d r B 2 which means that the magnetic equivalent of the electric charge element dq is, q 1 I 1 r s × ⇒ dq Id r s × ⇒ dq 2 I 2 d r s × . Using an analogy to the field due to the point charge dq 2 , d r E 2 = k dq 2 r 2 ˆ r d r B 2 = k m I 2 d r s × r 2 ˆ r r B 2 = k m I 2 d r s × ˆ r r 2 . This is called the Biot-Savart Rule. r B = μ o 4 π Id r s × ˆ r r 2 The Biot-Savart Rule The magnetic constant is usually replaced with k m = μ o 4 π 10 - 7 T m A .
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Physics 4B Lecture Notes 30-2 Example 1: Find the magnetic field due to a long straight wire carrying a current I. Starting with the Biot-Savart Rule,
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Ch30 - Physics 4B Lecture Notes Chapter 30 Magnetic Fields...

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