The distance between the plates of a parallel plate capacitor is `0.04m` A field of `5000V//m` is established between the plates and an unchanged metal plate of thickness `0.01m` is inserted intothe condenser parallel to its plate. Find the `p.d`. between the plates (a) before the introducing of the metal plate and (b) after its introduction. what would be the `p.d.` if plate of dielectric constant `K=2` is introduced in place of metal plate?

Explanation

`p.d`. Across capacitor `V=Ed=5000xx0.04=200V`
`C=(Ain_(0))/(d)=(Ain_(0))/(0.04)`
`V=200V`
`C'=(Ain_(0))/(d-t+(t)/(K))=(Ain_(0))/(0.04-0.01+(0.01)/(oo))=(Ain_(0))/(0.03)`
`V'=?`
Since charge remains same
`Q=CV=C'V"`
`(Ain(0))/(0.04)xx200=(Ain_(0))/(0.03)V'implies V'=150V`
`C"=(Ain_(0))/(d-t+(t)/(K))=(Ain_(0))/(0.04-0.01+(0.01)/(2))=(Ain_(0))/(0.035)`
`Q=CV=C"V"`
`(Ain_(0))/(0.04)xx200=(Ain_(0))/(0.035)V"`
`V"=175V`