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capacitance with two different dielectrics equation

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Capacitance with dielectric formula

Consider a parallel plate capacitor which is connected with a battery of emf ‘V’ .Let ‘A’ is the area of each plate and ‘d’  is separation between the plates.

If ‘q’ charge is stored in the capacitor when there is vacuum or air as medium between the plates ,then:

q= CV

Where ‘C’ is the capacitance of the capacitor,which,for the case of parallel plate capacitor is expressed as:

capacitance of dielectric

Michael Faraday,in 1937,investigated that if the space between the plates of parallel plate capacitor is filled with some dielectric medium ,then the charge stored in the capacitor increased to ‘q’.And hence ,the capacitance of the capacitance also increases to ‘C’.

Dielectrics

Dielectrics are the insulating materials through which the electric current cannot pass easily,because these materials have very high value of electrical resistance.For example,paper,pyrex,polystyrene,transformer oil,pure water,silicon etc.

Difference between polar and non polar dielectrics

There are two types of dielectrics:

  1. Polar Dielectrics
  2. Non polar dielectrics

Polar dielectrics

The dielectric materials which have permanent electric dipoles moment ‘p’ are called polar dielectrics.These materials consists of molecules which are permanent dipoles.

In the absence of external electric field,the polar molecules are randomly oriented.As the result,these materials have no net dipole moment.

When the external electric field is applied,then all dipoles tend to align themselves with external electric field.But the thermal agitation tends to keep the dipoles randomly oriented.Hence the partial alignment of electric dipoles is produced in a polar dielectric medium for specific field strength.However,the alignment of dipoles can be increased by increasing the external electric field and decreasing the temperature.

Non polar dielectrics

non polar dielectric

The electric materials which don’t have permanent dipole moments are called non polar dielectrics.In the absence of external electric field,the atoms are neutral.When the electric field of strength ‘E0‘ is applied ,then it tends to separate to positive and negative charges on the atoms of molecules.As the result,the atoms and molecules of dielectric become dipoles,called induced dipoles and this process is called electric polarization.

If the non polar dielectric materials is placed in a electric field having strength ‘E0‘ then another electric field ‘E’ is produced due to polarization of medium.The electric field produced due to the polarization of dielectric is always opposite to the direction of external electric field.So,the net electric field in the region is ‘E=E0-E’. Hence,the net electric field is reduced due to polarization of dielectric medium.

Effect of Dielectric on capacitance formula

When there is no dielectric medium between the plates of capacitor ,the stored charge ‘q’ in the capacitor can be find out using expression:

q=CV

But when the dielectric medium is placed between the plates of capacitor,then the net electric field and net potential difference between the plates is reduced due to electric polarization of dielectric medium.Therefore,the battery does work to transfer more charge to increase the potential difference between the plates.Therefore,the more charge is stored in capacitor,when a dielectric medium is placed between its plates and hence the capacitance of capacitor increased.

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