Exercise 29.42 A parallel-plate air-filled capacitor is being charged as in the

Question

Exercise 29.42

A parallel-plate air-filled capacitor is being charged as in the figure (Figure 1) . The circular plates have radius 4.10cm , and at a particular instant, the conduction current in the wires is 0.280A .

Part A

What is the displacement current density jD in the air space between the plates?

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Part B

What is the rate at which the electric field between the plates is changing?

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Part C

What is the induced magnetic field between the plates at a distance of 1.93cm from the axis?

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Part D

What is the induced magnetic field between the plates at a distance of 1.07cm from the axis?

Exercise 29.42

A parallel-plate air-filled capacitor is being charged as in the figure (Figure 1) . The circular plates have radius 4.10cm , and at a particular instant, the conduction current in the wires is 0.280A .

Part A

What is the displacement current density jD in the air space between the plates?

jD =   A/m2  

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Part B

What is the rate at which the electric field between the plates is changing?

dEdt =   V/m?s  

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Part C

What is the induced magnetic field between the plates at a distance of 1.93cm from the axis?

B1 =   T

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Part D

What is the induced magnetic field between the plates at a distance of 1.07cm from the axis?

B2 = T

Exercise 29.42 A parallel-plate air-filled capacitor is being charged as in the figure (Figure 1) . The circular plates have radius 4.10cm , and at a particular instant, the conduction current in the wires is 0.280A . Part A What is the displacement current density jD in the air space between the plates? jD = A/m2 SubmitMy AnswersGive Up Part B What is the rate at which the electric field between the plates is changing? dEdt = V/m?s SubmitMy AnswersGive Up Part C What is the induced magnetic field between the plates at a distance of 1.93cm from the axis? B1 = T SubmitMy AnswersGive Up Part D What is the induced magnetic field between the plates at a distance of 1.07cm from the axis? B2 =

Explanation / Answer

Acapacitor being charged by a current i c has a displacement currentequal to i c between the plates

?displacementcurrent i D = i c

                                        = 0.280 A

radius of thecircular plate r = 4 cm

                                          = 0.04 m

(A ) . displacement current density j D = i D / ( ? r2 )

                                                            = 0.28 / ( 3.14 * 0.04 2 )

                                                            = 55.73 A / m 2

(B ) . displacement current density j D = ? ( dE / dt)

          the rate at which the electric field between the plates is changing( dE / dt ) = j D / ?

                                        dE / dt ) = 55.73 / 8.85 * 10-12

                                                        = 6.3* 10 12 N / C - s

(C ) . the induced magnetic field between the plates B = (? * r / 2? R 2 ) * i c ----( 1)

                               whereR = 1.93 cm

                                            = 0.0193 m

                                        r = 3.86 cm

                                           = 0.0386 m

                                         ? = permeability of free space

                                             =4? * 10 -7 H   

        

       substitute these values in equation ( 1 ) you getanswer

(D ) substitute R = 1.07 cm = 0.0107 m   in equation ( 1 ),we getanswer

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