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# E2HWCH30 - Chapter 30 Maxwells Equations and...

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Chapter 30 Maxwell’s Equations and Electromagnetic Waves 19 •• [SSM] There is a current of 10 A in a resistor that is connected in series with a parallel plate capacitor. The plates of the capacitor have an area of 0.50 m 2 , and no dielectric exists between the plates. ( a ) What is the displacement current between the plates? ( b ) What is the rate of change of the electric field strength between the plates? ( c ) Find the value of the line integral C d B , where the integration path C is a 10-cm- radius circle that lies in a plane that is parallel with the plates and is completely within the region between them. Picture the Problem We can use the conservation of charge to find I d , the definitions of the displacement current and electric flux to find dE / dt , and Ampere’s law to evaluate d B around the given path. ( a ) From conservation of charge we know that: A 10 d = = I I ( b ) Express the displacement current I d : [ ] dt dE A EA dt d dt d I 0 0 e 0 d φ = = = Substituting for dE / dt yields: A I dt dE 0 d = Substitute numerical values and evaluate dE / dt : ( 29 s m V 10 3 . 2 m 50 . 0 m N C 10 85 . 8 A 10 12 2 2 2 12 × = × = - dt dE ( c ) Apply Ampere’s law to a circular path of radius r between the plates and parallel to their surfaces to obtain: enclosed 0 C I d μ = B Assuming that the displacement current is uniformly distributed and letting A represent the area of the circular plates yields: A I r I d 2 enclosed = π d 2 enclosed I A r I π = Substitute for enclosed I to obtain: d 2 0 C I A r d π μ = B

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Substitute numerical values and evaluate C d B : ( 29 ( 29 ( 29 m T 79 . 0 m 50 . 0 A 10 m 10 . 0 A / N 10 4 2 2 2 7 C = × = - μ π π d B 19 •• [SSM] There is a current of 10 A in a resistor that is connected in series with a parallel plate capacitor. The plates of the capacitor have an area of 0.50 m 2 , and no dielectric exists between the plates. ( a ) What is the displacement current between the plates? ( b ) What is the rate of change of the electric field strength between the plates? ( c ) Find the value of the line integral C d B , where the integration path C is a 10-cm- radius circle that lies in a plane that is parallel with the plates and is completely within the region between them. Picture the Problem We can use the conservation of charge to find I d , the definitions of the displacement current and electric flux to find dE / dt , and Ampere’s law to evaluate d B around the given path. ( a ) From conservation of charge we know that: A 10 d = = I I ( b ) Express the displacement current I d : [ ] dt dE A EA dt d dt d I 0 0 e 0 d φ = = = Substituting for dE / dt yields: A I dt dE 0 d = Substitute numerical values and evaluate dE / dt : ( 29 s m V 10 3 . 2 m 50 . 0
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E2HWCH30 - Chapter 30 Maxwells Equations and...

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