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Chapter 20 Learning Objectives

*Note: Type-setting limitations do not allow for arrows on the vector labels, so we have used boldface only.

Concepts and Skills to Review

  • Electric potential (Section 17.2)
  • Capacitors and energy stored (Sections 17.5, 17.7)
  • Measuring currents and voltages (Section 18.9)
  • Magnetic fields and forces (Sections 19.1, 19.2, 19.8)

Summary

  • A conductor moving through a magnetic field develops a motional emf given by
     ξ = vBL(20-2a)
    if both v and B are perpendicular to the rod.
  • The emf due to an ac generator with one planar coil of wire turning in a uniform magnetic field is sinusoidal and has amplitude ωNBA:
     ξ(t) = ωNBA sin ωt(20-3b)
    Here ω is the angular speed of the coil, A is its area, and N is the number of turns.
  • Magnetic flux through a planar surface:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_5.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-5)
    The magnetic flux is proportional to the number of magnetic field lines that cut through a surface. The SI unit of magnetic flux is the weber (1 Wb = 1 T·m2).
  • Faraday's law gives the induced emf whenever there is a changing magnetic flux, regardless of the reason the flux is changing:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_6.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-6)
  • Lenz's law: the direction of an induced emf or an induced current opposes the change that caused it.
  • The back emf in a motor increases as the rotational speed increases.
  • For an ideal transformer,
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_9.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-9,10)
    The ratio N2/N1 is called the turns ratio. There is no energy loss in an ideal transformer, so the power input is equal to the power output.
  • Whenever a solid conductor is subjected to a changing magnetic flux, the induced emf causes eddy currents to flow simultaneously along many different paths. Eddy currents dissipate energy.
  • A changing magnetic field gives rise to an induced electric field. The induced emf is the circulation of the induced electric field.
  • A changing current in one circuit element induces an emf in another circuit element. The mutual inductance is the constant of proportionality between the rate of change of the current and the induced emf.
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_12.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-12)
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_13.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-13)
  • Self-inductance is when a changing current induces an emf in the same device:
     Φ = LI(20-14)
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_16.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (20-16)
  • The energy stored in an inductor is
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_17.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (20-17)
  • The energy density (energy per unit volume) in a magnetic field is:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_18.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (20-18)
  • Current through an inductor must always change continuously, never instantaneously. In an LR circuit, the time constant is:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58003/image20_22.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (20-22)
    The current in an LR circuit is:
     If I0 = 0, I(t) = If(1 - e-t/τ)(20-21)
     If If = 0, I(t) = I0e-t/τ(20-24)





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