Important revision notes of Chapter 2 - Electrostatic Potential and Capacitance are available in this article. Important concepts related to electrostatic potential are already covered in part I, in part II we will mainly focus on concepts related to dielectric and electric capacitance.
• Types of dielectrics
• Dielectric Polarization
• Capacitance of a Capacitor
• Capacitance of an Isolated Conducting Sphere
• Parallel Plate Capacitor and Its Capacitance
• Combination of Capacitors
• Effect of Conductors in Capacitor
• Effect of Dielectrics in Capacitor
• Energy Stored in Capacitor
• Total Energy of the combination of capacitors
• Energy Density or Energy per Unit Volume
• Common Potential of charge capacitors
• Energy dissipated when two charged capacitors are connected
Dielectrics are non-conducting substances. In contrast to conductors, they have no (or negligible number of) charge carriers.
Types of dielectrics:
Dielectrics are of two types:
(i) Non-Polar Dielectrics: When the centre of positive charge coincides with the centre of negative charge in a molecule, e.g., Nitrogen, Oxygen, CO2 etc.
(ii) Polar Dielectrics: When the centre of positive and negative charges do not coincide because of the asymmetric shape of the molecules, e.g., NH3, HCl etc.
In a dielectric, this free movement of charges is not possible. It turns out that the external field induces dipole moment by stretching or re-orienting molecules of the dielectric. The collective effect of all the molecular dipole moments is net charges on the surface of the dielectric which produce a field that opposes the external field. Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field. It only reduces it. The extent of the effect depends on the nature of the dielectric.
Image Source: NCERT Book
It is an arrangement of primarily two conductors for storing large amount of electric charge.
Capacitance of a Capacitor:
Capacitance (C) of a capacitor is defined as ratio of charge (Q) given to the potential difference (V) applied across the conductors, i.e., C = Q/V.
The SI unit of capacitance is farad (F).
Capacitance of an Isolated Conducting Sphere:
The capacitance (C) of an isolated conducting sphere of radius (r) is given by C = 4 π ∈o r.
Parallel Plate Capacitor and Its Capacitance:
A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. The two plates have charges Q and –Q.
Image Source: NCERT Book
Parallel plate capacitor is an arrangement of two large metal plates of area A each kept parallel to each other at a distance d apart. If the space between the plates is vaccum (or air) then the capacitance of such an arrangement is given by,
Combination of Capacitors
We can combine several capacitors of capacitance C1, C2,…, Cn to obtain a system with some effective capacitance C. The effective capacitance depends on the way the individual capacitors are combined. Two simple possible ways are:
Capacitors in Series:
In series arrangement the magnitude Q of charge on each plate is same
Capacitors in Parallel
In parallel arrangement the potential difference across the each capacitor will remain same.
CEquivalent = C1 + C2 + C3 . . . + Cn
Effect of Conductors in Capacitor
When a parallel plate capacitor is partially filled with a metallic slab of thickness t < d, its capacitance will be:
Effect of Dielectrics in Capacitor
When a dielectric slab of dielectric constant K having thickness t < d is placed between the plates of parallel plate capacitor.
The capacitance of the capacitor will be,
Energy Stored in Capacitor
Energy stored (U) in capacitor (C) charged to a potential difference V is given as,
Total Energy of the combination of capacitor:
Energy Density or Energy per Unit Volume:
The energy density or energy stored per unit volume of a charged capacitor is given by
Common Potential of charged capacitors
If C1and C2 are capacitors charged to potentials V1 and V2 respectively. These capacitors are connected by a conducting wire, charges flow from higher potential to lower potential. This flow of charge will continue till their potentials become equal. There will no charge is lost in sharing and their common potential is given by,
Energy dissipated when two charged capacitors are connected
If U1 is the total energy before sharing of charges and U2 is total energy after sharing of charges then,