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Thursday, 2 March 2017

Electrostatic Potential and Capacitance - II


Capacitance C of a System of Two Conductors Separated by an Insulator:

It is defined as,
where Q and – Q are the charges on the two conductors V is the potential difference between them.
Capacitance is determined purely geometrically, by the shapes, sizes, and relative positions of the two conductors.

Capacitance C of a parallel plate capacitor (with vacuum between the plates):

where A is the area of each plate and d the separation between them.

For capacitors in the series combination:

The total capacitance C is

For capacitors in the parallel combination:

The total capacitance C is

where C1,C2,C3... are individual capacitances

The energy U stored in a capacitor of capacitance C, with charge Q and voltage V:


The electric energy density (energy per unit volume) in a region with electric field:

The potential difference between the conductor (radius ro) inside & outside spherical shell (radius R):


When the medium between the plates of a capacitor filled with an insulating substance:

Changes observed are as follows:

i. Polarization of the medium gives rise to a field in the opposite direction.
ii. The net electric field inside the insulating medium is reduced.
iii. Potential difference between the plates is thus reduced.
iv. Capacitance C increases from its value when there is no medium (vacuum). where K is the dielectric constant of the insulating substance.

Electrostatic Shielding:

A conductor has a cavity with no charge inside the cavity, then no matter what happens outside the conductor. Even if there are intense electric fields outside the conductor, the cavity inside has, shielding whatever is inside the cavity from whatever is outside the cavity. This is called electrostatic shielding.

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