Question

In an isolated, charged, parallel plate air capacitor, the surface charge density on each plate has a magnitude $\sigma$. A dielectric slab with dielectric constant K is now introduced between the plates. The induced charge per unit area on the surface of the dielectric will be :

• A. $\frac{\sigma }{K}$
• B. $\sigma (K-1)$
• C. $\sigma [1-\frac{1}{K}]$
• D. $\frac{\sigma }{K+1}$

Answer 1

The correct option is C $\sigma [1-\frac{1}{K}]$

When dielectric is placed inside the capacitor, the equation follows:
$E_i=\frac{\sigma }{{ϵ}_0}-\frac{\sigma }{K{ϵ}_0}$
which gives the charge induced as :
$\sigma [1-\frac{1}{K}]$