State the principal of the device that can build up high voltages of the order of a few million volts. Draw its labelled diagram.A stage reaches in this device when the potential at the outer cannot be increased further by piling up more charge on it. explain why.
Answers
Van de Graff generator is the device used for building up high potential differences of the order
of a few million volts.
Such high potential differences are used to accelerate charged particles such as electrons,
protons, ions, etc.
It is based on the principle that charge given to a hollow conductor is transferred to outer
surface and is distributed uniformly over it.
It consists of a large spherical conducting shell (S) supported over the insulating pillars. A long
narrow belt of insulating material is wound around two pulleys P1 and P2. B1 and B2 are two
sharply pointed metal combs. B1 is called the spray comb and B2 is called the collecting comb.
Working – The spray comb is given a positive potential by high tension source. The positive
charge gets sprayed on the belt.
As the belt moves and reaches the sphere, a negative charge is induced on the sharp ends of
collecting comb B2 and an equal positive charge is induced on the farther end of B2.
This positive charge shifts immediately to the outer surface of S. Due to discharging action of
sharp points of B2, the positive charge on the belt is neutralized. The uncharged belt returns
down and collects the positive charge from B1, which in turn is collected by B2. This is
repeated. Thus, the positive charge on S goes on accumulating. In this way, voltage differences
of as much as 6 or 8 million volts (with respect to the ground) can be built up.
The main limiting factor on the value of high potential is the radii of sphere.
If the electric field just outside the sphere is sufficient for dielectric breakdown of air, no more
charge can be transferred to it.
For a conducting sphere,
Electric field just outside sphere
E = Q
4\pi\epsilon R^2
and electric potential
V = Q
4\pi\epsilon R
Thus, E = VR
Now, for E = 3 * 10^6 V/m (dielectric breakdown)
Radius of should be 1 m.
Thus, the maximum potential of a sphere of radius 1 m would be 3 * 10^6 V.