Capacitance Assignment Help

Electrostatics - Capacitance

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A conductor is a substance that can be used to carry or conduct electric charge from one place to the other. All metals, for example are foods conductors of electricity. This is because conductors contain free charge carriers (free electrons).

Some of the important results regarding electrostatics of conductors are discussed below:
Inside a conductor, electric filed is zero.

Suppose a conductor ABCD is held in an external electric field of intensity ~Eo free electrons in the conductor move from AB to C.

As a result some net negative charge appears on CD and an equal positive charge appears on AB. There are called induced charges. They produce an induced electric field of intensity  ~Ep which opposes the flow of free electrons form AB to CD. The flow therefore, stops as soon as  ~Ep becomes equal to  ~Eo  as the applied filed and induced electric field inside the conductor are equal and opposite therefore, net electric field in the interior of the conductor is zero.

The interior of a conductor can have no excess charge in static situation. 

Let us consider any arbitrary volume element V inside a charged conductor. On the closed surface S bounding this volume element, electrostatic field is zero. Therefore, total electric flux through S is zero. by gauss’s theorem there is not net charge enclosed by S as volume V and surface S bounding it can be made as small as possible therefore, there is not net charge at any point in the interior of the conductor. The excess charge, if any must reside on the outer surface of the conductor. 

Electric filed justoutdie a charged conductor is perpendicular to the surface of the conductor at every point under electrostatic conditions, once the charge son a conductor are rearranged, the flow of charges stops . Therefore, component of electric filed along the tangent to the surface of the conductor must be zero.

E cos θ  = 0, where θ is the angle which electric field intensity makes with the tangent to the surface. 

Electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface.

As electric filed  ~E = 0 inside the conductor no work is done in moving a small test charge within the conductor. Therefore, there is no potential difference between any two points inside the conductor electrostatic potential is constant throughout the volume of the conductor. 

Further  ~E is perpendicular to the surface of the conductor. Therefore  ~E has no tangential component on its surface no work is done in moving a test charge on the surface of the conductor. Hence, there is electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface. 
Electric filed at the surface of a charged conductor is  ~Eo  = σ / , where σ is surface charge density and n is a unit vector normal to the surface in the outward direction. 

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