Electrical capacitance

Electrical capacitance

In this topic we will discuss about the Electrical capacitance and electrostatics of conductor,electrostatic shielding  , and the capacity of an isolated spherical conductor .

Electrostatics of conductor

As we know a conductor is a substance through which electric charge can conduct from one point to another . But there is some important results regarding  electrostatics of conductor which are follows –

  1. In electrostatic equilibrium , electric field is zero every where inside the conductor . Suppose a conductor ABCD is held in an external electric field of intensity E0 as shown in figure , the free electrons in the conductor moves from AB to CD . As a result , some net negative charge appears on AB . and the produced electric field Ep , which opposes the flow of free electrons from AB to CD . since Ep = E0 so net field inside the conductor is zero .

  1. The electric field just outside the charged conductor is perpendicular to the surface of the conductor at every point .
  2. Net charge in the interior of the conductor is zero .

According to Gauss’s law  ∫E.ds =q/ϵ0 ];

since inside the conductor E=0

therefore q= 0 also ;

  1. Electric field at the surface of the charged conductor is given as E = σ/ϵ0 where σ is the surface charge density . and the surface charge density is different at different point for irregular shaped conductor .

ELECTROSTATIC SHIELDING –

 It is the phenomenon to protect a space or an object from external electric field by covering it by conducting substance . as we know electric field inside a conductor is zero hence when an object is placed inside the conductor then there is no electric field connected to the object which is inside the conductor .

Electrical capacitance

Electrical capacitance of a conductor is the ability of the conductor to store electric charge in it.

When conductor given some charge then its potential increases . Let Q is the charge given to the conductor then its potential increases to V volt so , we can say,   Q α V  or , Q = CV ; where C is a constant called capacity of the conductor , we can write  capacity C = Q/V  , Using this expression we can write , capacity of a conductor is the ratio of charge given to the potential developed in the conductor i.e. C = Q/V ;

 

In another way we can define , electrical capacity of a conductor is numerically equal to the charge required to increase the potential by unit volt .      Its unit is farad (F)

Here 1 Farad =1 coulomb/1 volt and its dimension is [ M-1L-2T4A2]

CAPACITY OF AN ISOLATED SPHERICAL CONDUCTOR

Suppose a conductor of radius ‘r’ with centre ‘O’ has given charge ‘Q’  then its potential increases by ‘V’ . here potential V= q/4∏ϵ0r

As we know capacity C = Q/V = Q/( q/4∏ϵ0r) Or. C = 4∏ϵ0r  ; Here r is in meter and  C is in farad .

As we can see C α r i.e larger the radius of the sphere and larger will be capacity of the conducting sphere .

Using this formula we can find the capacity of the earth which is given as

C= 4×3.14 x(1/9×109) x 6.4x 106 = 711 x 10-6F  or 711μF .

For next topic of electrostatics  which is parallel plate capacitor -click here –

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