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Calculate the capacitance of a parallel...

Calculate the capacitance of a parallel plate condenser, with plate area A and distance between 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?

Text Solution

Verified by Experts

The correct Answer is:
`C=(A beta)/(2ln(1+(betad)/(2in_(0)))),betad=4in_(0)l n(1+(betad)/(2in_(0)))`. Solution of this equation gives required value of `beta`.
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