5. -11 points HRW9 32 P.O18 My Notes Ask Your The circuit in the figure below co

Question

5. -11 points HRW9 32 P.O18 My Notes Ask Your The circuit in the figure below consists of switch S, a 12.0 V ideal battery, a 16.0 M resistor, and an air-filled capacitor. The capacitor has parallel circular plates of radius 6.00 cm, separated by 3.00 mm. At time t 0, switch S is closed to begin charging the capacitor. The electric field between the plates is uniform. At t 250 us, what is the magnitude of the magnetic field within the capacitor, at radial distance 3.00 cm? Read the eBook Section 32-4 Displacement Current Submit Answer Progress Practice Another Version 6. 0 -12 points HRWO 32.P.019 My Notes Ask Your Teacher

Explanation / Answer

Given

voltage   V =   12 V

resistance of the resistor   R = 16*106

radius of circular plates r = 6 cm = 0.06 m

seperation between plates d = 3 mm = 3*10-3 m

capacitance of the capacitor is

         C = o A / d

               = ( 8.85* 10 -12 ) ( *0.06 2 ) / ( 3*10 ^ -3 )

               = 3.336 *10-11 F

time constant of the circuit is  

          = RC

               = ( 16*106) (3.336*10-11 F)

               =5.33*10-4 s

Displacement current  

          i = ( V / R ) ( e ^ - t / )

              = ( 12 / 16*10 ^6 ) ( e - 2.5*10^-4 s   / 5.33*10^ -4 s )

= 4.692*10 ^ -7 A

magnetic field with in the capacitor is

         B = o i r / 2 R 2    

             = ( 4*10-7 ) ( 4.962*10-7 A ) ( 0.03) / 2 ( 0.06 ) 2

              = 8.26*10-13 T  

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