question_answer

Direction (Q. Nos. 24) A parallel plate capacitor is as shown in figure. Half of the region in between the plates of the capacitor is filled with a dielectric material of dielectric constant K and in the remaining half air is present. The capacitor is given a charge Q with the help of a battery. Some surfaces are marked on the figure.

Surface I is the right half inner surface of the upper plate of capacitor in tire region in which air is present.

Surface II is the left half inner surface of the upper plate of capacitor.

Surface III is the surface of the dielectric slab which is near to the upper plate of capacitor.

Based on above information answer the following questions:

The charge on surface I is

A)  \[\frac{Q}{2}\]                                 

B)  \[\frac{Q}{1+K}\]

C)  \[\frac{KQ}{1+K}\]                         

D)  \[\frac{Q}{K-1}\]

Correct Answer: B

Solution :

 Divide the charge \[Q\] on two capacitors. \[{{Q}_{2}}=\frac{Q\times {{C}_{0}}}{K{{C}_{0}}+{{C}_{0}}}=\frac{Q}{K+1}\]