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| Electrostatics of Conductor |
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| All materials are broadly classified into two categories, one conductors and other insulators. When a conductor is placed in a electric field, there is a large scale of physical movement of free electrons, within the conductor and they move out only if we make arrangements for it. |
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| Insulators are called dielectrics. There are no free electrons and they remain electrically neutral, the individual molecules remain undistributed. Glass, oil, stone, etc. are few examples of dielectrics. |
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| In an electrostatic situation, the following conditions are applicable to conductors. |
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| (i) Within a conductor, both the electric field and volume density of charge vanish. |
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| (ii) Just outside the surface, the electric field acts at right angles to the surface. |
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| 1. Inside a conductor, electro static field is zero. |
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| A conductor has free electrons, and they experience a force only when the electric field is not zero. In a static situation, the free electrons gets itself distributed in such a way that, the electric field everywhere inside the conductor is zero. |
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| 2. At the surface of a charged conductor, electrostatic field must be normal to the surface at every point. |
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| If the electric field is not normal to the surface, then it would have same non-zero component along the surface. The free charges on the surface would then experience a force and move. In a static situation, electrostatic field should not have tangential component, which in turn implies that the surface of a charged conductor must be normal to the surface at every point. If a conductor has no surface charge, then the field is zero. |
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| 3. The interiors of a conductor can have no excess charge in static situation |
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| In a static situation, when a conductor is charged, the excess charges reside only on the surface. If we consider any arbitrary volume inside a conductor, the electrostatic field on closed surface bounding the arbitrary volume is zero. Thus, the flux through the surface is zero. By Gauss's theorem, there is no net charge enclosed by closed surface. If the surface and volume is made very small, it shows that there is no net charge inside and no excess charge can reside on the surface. |
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| 4) Electrostatic Potential is a constant throughout the volume of a conductor and has the same value inside and on its surface. |
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| As we know, the electrostatic field inside the conductor is zero and on the surface, the electrostatic field is normal to the surface at every point. No work is done in moving a small test charge, within the conductor and on its surface. We find there is no potential difference between the two points inside or on the surface, which implies the potential being constant throughout. |
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| If a conductor is charged, electric field normal to the surface exists, which means potential will be different for the surface and a point just outside the surface. Each conductor is characterised by a constant value of potential. But this constant differs from conductor to conductor. |
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| 5. Electric field at the surface of a charged conductor |
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The electric field  where 's'
is the surface charge density and 
the unit vector normal to the surface in the outward direction. Choose a small cylinder, which is partly inside and partly outside the surface of the conductor. The small area of cross section is 'ds', and take height as negligible. We know just inside the surface, the electrostatic field is zero and just outside, the field is normal to the surface. Thus, the flux through the small cylinder is only from the
outside, which is ± E.ds
(positive when charge density 's' is greater than zero and negative when 's' is lesser than zero). 'E' is considered constant for a small area of 'ds', E and ds are parallel. |
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| Thus the equation
is true for both signs of 's' when s
> 0, electric field is normal to the surface outward and when s<0, electric field is normal to the surface inward. |
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| 6. Electrostatic Shielding |
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| This technique is used by many electrical instruments from outside electrical influence. |
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| Consider a conductor with a cavity and no charges in the cavity. Then, the remarkable result is that whatever the shape, size of the cavity and whatever be the charge on the conductor, whatever the external electric field it may be placed, the electric field inside the cavity remains zero. In our earlier topics, we have already seen that field inside a charged spherical shell is zero. The vanishing of electric field in the charge free cavity of a conductor is a general result. We also know that charges reside on the surface of the conductor. Whatever be the cavity and field configuration outside, cavity remains shielded from the electric field and this is referred to as electrostatic shielding. |
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