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Chapter 29:Electromagnetic Induction and Faraday’s Law 28-4 Ampère’s Law Example 28-8: A nice use for Ampère’s law. Use Ampère’s law to show that in any region of space where there are no currents the magnetic field cannot be both unidirectional and nonuniform as shown in the figure. Problem 27 27. a (I) A 2.5-mm-diameter copper wire carries 33-A current (uniform across its cross section). Determine the magnetic field: (a) at the surface of the wire; (b) inside the wire, 0.50 mm below the surface; (c) outside the wire 2.5 mm from the surface. 28-4 Ampère’s Law Solving problems using Ampère’s law: • Ampère’s law is only useful for solving problems when there is a great deal of symmetry. Identify the symmetry. • Choose an integration path that reflects the symmetry (typically, the path is along lines where the field is constant and perpendicular to the field where it is changing). • Use the symmetry to determine the direction of the field. • Determine the enclosed current. 28-5 Magnetic Field of a Solenoid and a Toroid A solenoid is a coil of wire containing many loops. To find the field inside, we use Ampère’s law along the path indicated in the figure. 28-5 Magnetic Field of a Solenoid and a Toroid The field is zero outside the solenoid, and the path integral is zero along the vertical lines, so the field is (n is the number of loops per unit length) 𝑩 = 𝝁𝟎 𝑛𝐼 N: number of Turns l: length 28-5 Magnetic Field of a Solenoid and a Toroid Example 28-9: Field inside a solenoid. A thin 10-cm-long solenoid used for fast electromechanical switching has a total of 400 turns of wire and carries a current of 2.0 A. Calculate the field inside near the center. 28-6 Biot-Savart Law The Biot-Savart law gives the magnetic field due to an infinitesimal length of current; the total field can then be found by integrating over the total length of all currents: 28-6 Biot-Savart Law Example 28-11:BB due to current I in straight wire.For the field near a long straight wire carrying a current I, show that the Biot-Savart law gives B = μ0I/2πr. Problem 37 37. (II) A wire is formed into the shape of two half circles connected by equal-length straight sections as shown in Fig. 28–45. A current I flows in the circuit clockwise as shown. Determine (a) the magnitude and direction of the magnetic field at the center, C, and (b) the magnetic dipole moment of the circuit. 29-1 Induced EMF https://www.youtube.com/watch?v=gfJG4M4wi1o 29-1 Induced EMF Almost 200 years ago, Faraday looked for evidence that a change in a magnetic field would induce an electric current with this apparatus: 29-1 Induced EMF He found no evidence when the current was steady, but did see a current induced when the switch was turned on or off.