Question

4. A parallel plate air capacitor is given a charge of 3 uC. A sheet of dielectric constant 3 is inserted so that it completely fills the gap between the plates. The induced charge on each face of the sheet is numericaly: (a) 2 uc (b) 3 C (c) 0 (d) 9 uc​

Answer 1

Given info : A parallel plate air capacitor is given a charge of 3 μC. A sheet of dielectric constant 3 is inserted so that it completely fills the gap between the plates.

To find : the induced charge on each face of the sheet is numerically is ..

solution : if a dielectric slab of dielectric constant K is placed between the gap of plates carrying charge q, the induced charge q' on the surface of slab is given by, $q'=q\left[\frac{K-1}{K}\right]$

here, q = 3 μC and K = 3

so, the induced charge on each face of the sheet is $3\mu C\left[\frac{3-1}{3}\right]=2\mu C$

therefore the induced charge on each face of the sheet is 2$\mu$C. hence option (a) is correct choice.