write the working process of vande Graff generator
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Answer:
Working principle of Van de Graaff Generator
Let us consider a large spherical shell of radius R. If we place a charge of magnitude Q on such a sphere, the charge will spread uniformly over the surface of the sphere and the electric field inside the sphere will be equal to zero, and that outside the sphere will be due to the charge Q placed at the centre of the sphere.
So the potential outside is that of a point charge; and inside it is constant, namely the value at the radius R. We thus have:
Potential inside conducting spherical shell of radius R carrying charge Q = constant and is given by,
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Let a small sphere be placed at the center of the large one such that the radius of the smaller sphere is r and the charge over its surface is q. The potential energy thus generated due to the smaller surface at different points in the system can be given as the following values,
At the surface of the small sphere:
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At the large spherical shell of radius R:
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If we consider the total charges in the system, that is, q and Q, then the total potential energy due to the system of charges can be given as,
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Assuming that q is positive, the inner sphere is always at a higher potential and is independent of the charge Q that is accumulated on the larger surface. The difference in potential given by the value V(r)-V(R) is positive. The potential due to Q is constant up to radius R and thus, the difference gets canceled out. If we connect the smaller and the larger sphere with a conducting wire, the charge q, however small, on the smaller sphere gets transferred to the bigger sphere. Here, if we introduce a small charged sphere into a larger spherical shell, as shown in the system, the charge on the larger sphere keeps increasing. Similarly, the potential at the larger sphere would also keep rising as the charge increases, until the breakdown field of air is reached. The Van de Graaff generator works on the same principle.