Chapter 25, Problem 071 A slab of copper of thickness D 1.3 mm 1s thrust into a

Question

Chapter 25, Problem 071 A slab of copper of thickness D 1.3 mm 1s thrust into a para plate capacitor of plate area A-6.6 cm2 and p a separation d 5.40 mm, as shawn in the figure; the slab is exac y halfway between the plates a) i hat is the capacitance after the dab isi f a pctential differencc A-65.0 V ts maintained between the plates, what is the ratio cf the stored cnergy befare o that after the slaDISInserted? (c) How much worl( 1s done on the slab as it is inserted? d) is thc dab sucked in or must it be pushed In? rduoed? b (a) Number (h) Number (c) Number Units Units Click if you would like to Show Work for this question: Open Show Work

Explanation / Answer

a)

Equivalent capacitance after slab is inserted

1/C =1/eoA/((d-b)/2) +1/eoA/((d-b)/2)

C=eoA/(d-b) =(8.8542*10-12)(6.6*10-4)/(5.4-1.3)*10-3

C=1.4253*10-12 F

b)

Ui/Uf =(1/2)(Q2/Ci)/(1/2)(Q2/Cf) =(eoA/d)/(eoA/d-b)=(d-b)/d =(5.4-1.3)/5.4 =0.76

c)

W=(1/2)(Cf-Ci)V2 =(eoA/2)[1/(d-b) -1/d]*V2

W=(8.85*10-12)(6.6*10-4/2)(103/4.1-103/5.4]*652

W=7.25*10-10 J

d)

Slab is sucked in

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