Capacitor Metal Sphere

Description:

Let there is a metal sphere and some charge ‘Q’ is given to it ,and for the displacement of each consecutive charge within the sphere, more energy is given to the charge or more work is done on each charge against the force of  repulsion.  Charges within the sphere does not escape and moves out because, air in its surrounding is dielectric (bad conductor). Hence air resists the flow of charges.

As the charge increases within the sphere, the potential as well as the energy of the sphere increases. This energy cannot be increased after a finite limit or in other words, we cannot give infinite charge to a conductor because, if the charge within the sphere increases, the potential increases and hence the electric field around the sphere becomes stronger. After a certain limit, electric field becomes very strong and crosses breakdown field. In such condition, negative charge of the air molecule present in the surrounding of the sphere are pulled towards the sphere to neutralize its additional positive charge, thereby ionizing air molecules. So as the electric field increases beyond a certain limit, air starts behaving like a conductor. This phenomenon of ionizing air molecule is called break down of insulator.  During break down of insulation, it is found that the charge stops increasing within the sphere but starts leaking into the surrounding. In that case the potential of metal sphere remains constant and gives the limit of charges stored within the conductor.

Charge with in the sphere = Q

Potintal of sphere = V

Breakdown field E = 1/4πε₀ Q/R²

Leaking of Charge

The phenomenon in which the charge within a metal stops increasing, by nullifying each additional charge and there by ionizing the air molecules in the surrounding of metal is called leaking of charges.

Breakdown field or Dielectric strength

The minimum value of electric field over a medium at  which, molecules of the any dielectric medium starts getting ionized.

Break down field for air is 10⁶V m^-1. It means that the air molecule will not be ionized at electric field below 10⁶V m^-1

Note

• If Dielectric strength of a medium is more, then more charges can be stored within the conductor.

• If Dielectric strength of a medium is more, the maximum potential of the conductor will be more.