Sources of Magnetic Field
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1 Chapter 28 Sources of Magnetic Field PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson
2 Goals for Chapter 28 To determine the magnetic field produced by a moving charge To study the magnetic field of an element of a current-carrying conductor To calculate the magnetic field of a long, straight, current-carrying conductor To study the magnetic force between currentcarrying wires To determine the magnetic field of a circular loop To use Ampere s Law to calculate magnetic fields
3 Introduction What can we say about the magnetic field due to a solenoid? What actually creates magnetic fields? We will introduce Ampere s law to calculate magnetic fields.
4 The magnetic field of a moving charge A moving charge generates a magnetic field that depends on the velocity of the charge. Figure 28.1 shows the direction of the field.
5 Magnetic force between moving protons Example 28.1 Two protons move parallel to the x-axis in opposite directions at the same speed v. Find the electric and magnetic forces on the upper proton and compare their magnitudes.
6 Magnetic field of a current element The total magnetic field of several moving charges is the vector sum of each field. Equation 28.7 is called the law of Biot and Savart.
7 Magnetic field of a straight current-carrying conductor If we apply the law of Biot and Savart to a long straight conductor, the result is B = 0 I/2πx. See Figure 28.5 below left. Figure 28.6 below right shows the right-hand rule for the direction of the force.
8 Magnetic fields of long wires Example 28.4 the magnetic field from two parallel wires.
9 Force between parallel conductors The force per unit length on each conductor is F/L = 0 II L/2πr. (See Figure 28.9 at the right.) The conductors attract each other if the currents are in the same direction and repel if they are in opposite directions.
10 Forces between parallel wires Example 28.5 What is the force per length below.
11 Magnetic field of a circular current loop The Biot Savart law gives B x = 0 Ia 2 /2(x 2 + a 2 ) 3/2 on the axis of the loop.
12 The Magnetic Field of a Solenoid N-loops (turns) At the center of N loops, x=0, the field on the axis is B x = 0 NI/2a. Where is x=0 in the figure?
13 Example 28.6 A coil consists of 100 circular loops with radius 0.60 m carries a 5.0 A current. (a) Find the magnetic field at the center, x=0. (b) Find the magnetic field at a point along the axis 0.80 m from the center (c) Along the axis, at what distance from the center of the coil is the field magnitude 1/8 as great as it is at the center?
14 Magnetic field of a coil The direction of the magnetic field can be found using the righthand rule. Along the x-axis, the magnetic field drops off as we move away from center. B x NIa 2( x a ) /2 What is B at x=±a?
15 Ampere s law (special case) Follow the text discussion of Ampere s law for a circular path around a long straight conductor, using Figure below.
16 Ampere s law (general statement) Follow the text discussion of the general statement of Ampere s law, using Figures and below.
17 Magnetic fields of long conductors Follow Example 28.7 for a long straight conductor. Follow Example 28.8 for a long cylinder, using Figures and below.
18 Ampere s Law applied to the Field of a solenoid Example 28.9
19 Field of a toroidal solenoid A toroidal solenoid is a doughnut-shaped solenoid. Example 28.10
20 The Bohr magneton and paramagnetism Follow the text discussions of the Bohr magneton and paramagnetism, using Figure below. Table 28.1 shows the magnetic susceptibilities of some materials. Follow Example
21 Diamagnetism and ferromagnetism Figure at the right shows how magnetic domains react to an applied magnetic field. Figure below shows a magnetization curve for a ferromagnetic material.
22 Hysteresis Nonlinear behavior, a delayed response Follow Example
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