An empty parallel plate capacitor (vacuum in between the plates) is connected to

Question

An empty parallel plate capacitor (vacuum in between the plates) is connected to a battery of voltage V, and is charged completely with a total charge of Q. The separation between the plates is originally d, and is increased by a distance x. A dielectric with dielectric constant ? is inserted between the plates. A) What is the new charge on the plates, Q2? b) What dielectric value of K could you insert into the capacitor in order to keep the charge the same (i.e. Q=Q2)? Your answers should be in terms of only known values: Q, d, x, and ?

Explanation / Answer

a) at first capacitor is completely charged to Q. and Q=CV

when distance is increased by x, then new charge Q'= d*Q/(d+x)

when we insert ?

then new charge Q2= (?/(?+1))*d*Q/(d+x)

b) value of k=-(d+x)/x

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