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Parallel Plate Capacitor

Parallel Plate Capacitor

Parallel Plate Capacitor

    A parallel plate capacitor consisted of two large conducting plates separated by a small distance. When the battery is connected across the battery, the plates get charged and establish an electric field. The electric field inside the capacitor has a direction from the positive plate to the negative plate. 

The capacitance of Parallel Plate Capacitor Without Dielectric 

The capacitance of Parallel Plate Capacitor Without Dielectric

Consider a parallel plate capacitor of two large conducting plates separated by a small distance d. The area of each plate is A. The distance d is much smaller than area A. so we can write A>>d. 

To find the capacitance there are 3 steps to follow, first we want to find the electric field E , then the potential V and finally capacitance C using equation C=Q/V 

E →V →C=  Q/V


For finding the total electric field divided the entire area into 3, region 1, region 2 & region 3 like this.


Electric field in region 1, is the sum of EF due to positive plate and EF due to negative plate
Hence the electric field due to positive plate and electric field due to negative late are equal in magnitude but opposite in direction the net EF becomes zero

Electric field in region 3, is the sum of EF due to positive plate and EF due to negative plate
Hence the electric field due to positive plate and electric field due to negative late are equal in magnitude but opposite in direction the net EF becomes zero

Special case electric field in region 2
So total electric field Enet is 
Now we have to find the potential V 
For that, we can use the relation between E & V 
E=  dv/dr
Hence the electric field in region 2 is constant we can change dr  to d
E=  V/d

V=E d

V=σ/(ε ̥)  d


Finally by using equation C = Q/V 


capacitance depends upon

    the distance d between two plates

    the area A of  the plate


(Aε ̥)/d  is the capacitance of a parallel plate capacitor without the dielectric. Next we will see about the effect of dielectric on a capacitor. that is how capacitance will change if we introduce dielectric instead of vacuum.  


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