Calculate the capacitanceof a parallel plate condenser, withplate area A and distancebetween plates d, when filled with a dielectric whose dielectric constant varies as, K(x)=1+(beta x)/(in_(0)) "" 0 lt x lt (d)/(2), "" K(x)=1+(beta)/(in_(0))(d-x)"" (d)/(2) lt x lt d. For what value of beta would the capacity of the condenser be twice that when it is without any dielectric?

Calculate the capacitanceof a parallel plate condenser, withplate area

1.	Calculate the capacitanceof a parallel plate condenser, withplate area A and distancebetween plates d, when filled with a dielectric whose dielectric constant varies as, K(x)=1+(beta x)/(in_(0)) "" 0 lt x lt (d)/(2), "" K(x)=1+(beta)/(in_(0))(d-x)"" (d)/(2) lt x lt d. For what value of beta would the capacity of the condenser be twice that when it is without any dielectric?
Answer» ANSWER :`C=(A BETA)/(2ln(1+(betad)/(2in_(0)))),betad=4in_(0)l n(1+(betad)/(2in_(0)))`. SOLUTION of this equation GIVES requiredvalue of `beta`.

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