Chapter 28 - Chapter 28 Magnetic Induction Conceptual...

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2663 Chapter 28 Magnetic Induction Conceptual Problems 1 [SSM] ( a ) The magnetic equator is a line on the surface of Earth on which Earth’s magnetic field is horizontal. At the magnetic equator, how would you orient a flat sheet of paper so as to create the maximum magnitude of magnetic flux through it? ( b ) How about the minimum magnitude of magnetic flux? Determine the Concept ( a ) Orient the sheet so the normal to the sheet is both horizontal and perpendicular to the local tangent to the magnetic equator. ( b ) Orient the sheet of paper so the normal to the sheet is perpendicular to the direction of the normal described in the answer to Part ( a ). 2 At one of Earth’s magnetic poles, how would you orient a flat sheet of paper so as to create the maximum magnitude of magnetic flux through it? Determine the Concept ( a ) Orient the sheet so the normal to the sheet is vertical. ( b ) Any orientation as long as the paper’s plane is perpendicular to Earth’s surface at that location. 3 [SSM] Show that the following combination of SI units is equivalent to the volt: T m 2 s . Determine the Concept Because a volt is a joule per coulomb, we can show that the SI units s m T 2 are equivalent to a volt by making a series of substitutions and simplifications that reduces these units to a joule per coulomb. The units of a tesla are m A N : s A m N s m m A N s m T 2 2 = = Substitute the units of an ampere (C/s), replace m N with J, and simplify to obtain: C J s s C J s m T 2 = =
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Chapter 28 2664 Finally, because a joule per coulomb is a volt: V s m T 2 = 4 Show that the following combination of SI units is equivalent to the ohm: Wb A s . Determine the Concept Because a weber is a newton meter per ampere, we can show that the SI units Wb A s are equivalent to an ohm by making a series of substitutions and simplifications that reduces these units to a volt per ampere. Because a weber is a A m N : s A J s A A m N s A Wb 2 = = Substitute the units of an ampere and simplify to obtain: C A J s s C A J s A Wb = = Finally, because a joule per coulomb is a volt: A V s A Wb = = 5 [SSM] A current is induced in a conducting loop that lies in a horizontal plane and the induced current is clockwise when viewed from above. Which of the following statements could be true? ( a ) A constant magnetic field is directed vertically downward. ( b ) A constant magnetic field is directed vertically upward. ( c ) A magnetic field whose magnitude is increasing is directed vertically downward. ( d ) A magnetic field whose magnitude is decreasing is directed vertically downward. ( e ) A magnetic field whose magnitude is decreasing is directed vertically upward. Determine the Concept We know that the magnetic flux (in this case the magnetic field because the area of the conducting loop is constant and its orientation is fixed) must be changing so the only issues are whether the field is increasing or decreasing and in which direction. Because the direction of the
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