A) A slab of copper of thickness b = 1.364 mm is thrust into a parallel-plate ca

Question

A) A slab of copper of thickness b = 1.364 mm is thrust into a parallel-plate capacitor of C = 9.00×10-11 F of gap d = 9.0 mm, as shown in the figure; it is centered exactly halfway between the plates. What is the capacitance after the slab is introduced?

B) If a charge q = 8.00×10-6 C is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted?

C) How much work is done on the slab as it is inserted?

D) Is the slab pulled in or must it be pushed in?

pulled
pushed

Explanation / Answer

C = A/d

C' = A/(d-b)

C' = C * (d/(d-b)) = 9e-11 * (9e-3/(9e-3-1.364e-3)) = 1.06e-10 F

If a charge q = 3.00×10-6 C is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted?

U = 0.5 q^2/C = 0.5 * 8e-6*8e-6/9e-11 = 0.35 J

U' = 0.5 q^2/C' = 0.5 * 8e-6*8e-6/1.06e-11 = 0.302 J

U/U' = 0.35/0.302 = 1.18

How much work is done on the slab as it is inserted?

U - U' = = 0.054 J

Is the slab pulled in or must it be pushed in?

pulled in

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