Electrostatic Potential And Capacitance

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Electric Potential due to an Electric Dipole

The electric potential at any point in the space due to an electric dipole is given as below -
By substituting different angle between P and r, potential at various point can be calculated.

Potential Energy of a System of Charged Particles:

The general formula to calculate the potential energy of a system of charged particle is given as below-
Therefore, if n identical charges are placed equidistant from each other (identical charges placed at the corners of an equilateral triangle or square etc.) then the net potential energy is

Calculating capacitance in Case of Composite Dielectric:

The space between the plates of a capacitor is filled with a composite dielectric (dielectric constant K1, K2,...). The thickness of the dielectrics are d1, d2, d3 and so on. Then the resultant capacitance of the system can be easily obtained as shown below -

Capacitance of Parallel Plate Capacitor with a Conducting Slab between the Plates:

The space between the plates of a parallel plate capacitor is partially field with a conducting slab of thickness t. Then the net capacitance can be calculated as shown below -

Special Connection of Capacitor Plates:

Let there be n parallel plates and separation between any two consecutive plates is d. The plates are connected in the following manner (alternate plates are connected to common points). This system is equivalent to (n-1) parallel plate capacitors connected parallelly.