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Copyright © 2009 Pearson Education, Inc. Chapter 27 Magnetism

Copyright © 2009 Pearson Education, Inc. A uniform magnetic field is constant in magnitude and direction. The field between these two wide poles is nearly uniform Magnets and Magnetic Fields

Copyright © 2009 Pearson Education, Inc. Experiment shows that an electric current produces a magnetic field. The direction of the field is given by a right-hand rule Electric Currents Produce Magnetic Fields

Copyright © 2009 Pearson Education, Inc Electric Currents Produce Magnetic Fields Here we see the field due to a current loop; the direction is again given by a right-hand rule.

Copyright © 2009 Pearson Education, Inc. A magnet exerts a force on a current- carrying wire. The direction of the force is given by a right- hand rule Force on an Electric Current in a Magnetic Field; Definition of B

Copyright © 2009 Pearson Education, Inc. Internet hints…

Copyright © 2009 Pearson Education, Inc. The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation: This equation defines the magnetic field B. In vector notation : 27-3 Force on an Electric Current in a Magnetic Field; Definition of B

Copyright © 2009 Pearson Education, Inc. Vector Cross Product; The vector cross product is defined as: The direction of the cross product is defined by a right-hand rule:

Copyright © 2009 Pearson Education, Inc. Vector Cross Product; The cross product can also be written in determinant form:

Copyright © 2009 Pearson Education, Inc Vector Cross Product; Torque as a Vector Some properties of the cross product:

Copyright © 2009 Pearson Education, Inc. Unit of B : the tesla, T: 1 T = 1 N/A·m. Another unit sometimes used: the gauss ( G ): 1 G = T Force on an Electric Current in a Magnetic Field; Definition of B

Copyright © 2009 Pearson Education, Inc. Just for interest…

Copyright © 2009 Pearson Education, Inc Force on an Electric Current in a Magnetic Field; Definition of B Example 27-1: Magnetic Force on a current-carrying wire. A wire carrying a 30-A current has a length l = 12 cm between the pole faces of a magnet at an angle θ = 60°, as shown. The magnetic field is uniform at 0.90 T. What is the magnitude of the force on the wire?

Copyright © 2009 Pearson Education, Inc Force on an Electric Current in a Magnetic Field; Definition of B Example 27-2: Measuring a magnetic field. A rectangular loop of wire hangs vertically as shown. A magnetic field B is directed horizontally, perpendicular to the wire, and points out of the page at all points. The magnetic field is very nearly uniform along the horizontal portion of wire ab (length l = 10.0 cm) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward magnetic force (in addition to the gravitational force) of F = 3.48 x N when the wire carries a current I = A. What is the magnitude of the magnetic field B?

Copyright © 2009 Pearson Education, Inc. Example 27-3: Magnetic Force on a semicircular wire. A rigid wire, carrying a current I, consists of a semicircle of radius R and two straight portions as shown. The wire lies in a plane perpendicular to a uniform magnetic field B 0. Note choice of x and y axis. The straight portions each have length l within the field. Determine the net force on the wire due to the magnetic field B 0. See the book for the full solution (there are some tricks)