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Chapter 30

# Chapter 30 - Chapter 30 Maxwells Equations and...

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Chapter 30 Maxwell’s Equations and Electromagnetic Waves Conceptual Problems 1 [SSM] True or false: ( a ) The displacement current has different units than the conduction current. ( b ) Displacement current only exists if the electric field in the region is changing with time. ( c ) In an oscillating LC circuit, no displacement current exists between the capacitor plates when the capacitor is momentarily fully charged. ( d ) In an oscillating LC circuit, no displacement current exists between the capacitor plates when the capacitor is momentarily uncharged. ( a ) False. Like those of conduction current, the units of displacement current are C/s. ( b ) True. Because displacement current is given by dt d I e 0 d φ = , I d is zero if 0 e = dt d . ( c ) True. When the capacitor is fully charged, the electric flux is momentarily a maximum (its rate of change is zero) and, consequently, the displacement current between the plates of the capacitor is zero. ( d ) False. I d is zero if 0 e = dt d . At the moment when the capacitor is momentarily uncharged, dE / dt 0 and so 0 e dt d . 2 Using SI units, show that dt d I e 0 d = has units of current. Determine the Concept We need to show that dt d e 0 has units of amperes. We can accomplish this by substituting the SI units of 0 and dt d e and simplifying the resulting expression. A s C V V s C s V C N C s V N C s m m V m N C 2 2 2 = = = = = 3 [SSM] True or false: ( a ) Maxwell’s equations apply only to electric and magnetic fields that are constant over time. 2829

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Chapter 30 2830 ( b ) The electromagnetic wave equation can be derived from Maxwell’s equations. ( c ) Electromagnetic waves are transverse waves. ( d ) The electric and magnetic fields of an electromagnetic wave in free space are in phase. ( a ) False. Maxwell’s equations apply to both time-independent and time- dependent fields. ( b ) True. One can use Faraday’s law and the modified version of Ampere’s law to derive the wave equation. ( c ) True. Both the electric and magnetic fields of an electromagnetic wave oscillate at right angles to the direction of propagation of the wave. ( d ) True. 4 Theorists have speculated about the existence of magnetic monopoles , and several experimental searches for such monopoles have occurred. Suppose magnetic monopoles were found and that the magnetic field at a distance r from a monopole of strength q m is given by B = ( μ 0 /4 π ) q m / r 2 . Modify the Gauss’s law for magnetism equation to be consistent with such a discovery. Determine the Concept Gauss’s law for magnetism would become inside m, 0 S n q dA B = where q m, inside is the total magnetic charge inside the Gaussian surface. Note that Gauss’s law for electricity follows from the existence of electric monopoles (charges), and the electric field due to a point charge follows from the inverse-square nature of Coulomb’s law.
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Chapter 30 - Chapter 30 Maxwells Equations and...

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