S L Arora Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 6: Text Based Exercises

A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

Define the terms the capacitance of a capacitor. When a dielectric is inserted between the plates of a charged parallel plate capacitor, fully occupying the intervening region, how does the polarization of the dielectric medium affect the net electric field? For linear dielectrics, show that the introduction of a dielectric increases its capacitance by a factor $k$, characteristic of the dielectric.

Define the terms dielectric strength of a dielectric. When a dielectric is inserted between the plates of a charged parallel plate capacitor, fully occupying the intervening region, how does the polarization of the dielectric medium affect the net electric field? For linear dielectrics, show that the introduction of a dielectric increases its capacitance by a factor $k$, characteristic of the dielectric.

Find the expression for the capacitance of a parallel plate capacitor of area $A$ and plate separation $d$ if a dielectric slab of thickness $t$. In which case would the capacitance be more and why?

Find the expression for the capacitance of a parallel plate capacitor of area $A$ and plate separation $d$ if a metallic stab of thickness $t$, where $(t<d)$ are introduced one by one between the plates of the capacitor. In which case would the capacitance be more and why?

What is the dielectric? A dielectric slab of thickness $t$ is kept between the plates of a parallel plate capacitor separated by distance $d$. Derive the expression for the capacitance of the capacitor for $t<<d$.

A small sphere, of radius $‘a’$, carrying a positive charge $q$, is placed concentrically inside a larger hollow conducting shell of radius $b(b>a)$. This outer shell has a charge $Q$ on it. Show that if these spheres are connected by a conducting wire, charge will always flow from the inner sphere to the outer sphere, irrespective of the magnitude of the two charges.

Name the machine which makes use of this principle. Draw a simple labelled line diagrams of this machine. What’s ‘practicle difficulty’ puts on upper linit on the maximum potential difference which this machine can built up?