Question

Explain the principle of the device that can build up high voltage of the order of a few million volts. Draw a schematic diagram and explain the working of this device. Are there any restrictions on the upper limit of the high voltage set up in this machine? Explain.

Answer 1

Hint: Van de Graff generator is the device which is able to produce a potential difference of high voltage. It is based on the capacitance or capacity and induction of spherical conductors. It is also known as particle accelerator in physics research because in this generator particle moves very fast in an evacuated tube due to high potential difference.

Complete step by step answer:
It is based on the principle that how the hollow spherical conductor carries or spreads it charges across its surface. And also based on the electrical capacity of the conductor in which charge is stored.

We can see that there is a belt in which the sub-particles get stuck. It consists of a large spherical conducting shell supported over the insulating pillars. A long narrow belt of insulating material is wound around two pulleys and two sharply pointed metal combs. And there are two combs which act as electrodes. These are called the spray comb and collecting comb.
There are very sharp points in the combs then the concentration of charges causes charge wind, and charges are stuck over the rotating belt. The spray comb is given a positive potential by a high tension source. As the belt rotates then the negative charge becomes induced at the collecting comb and an equal positive charge is induced on the farther end of the spherical round conductor. This positive charge shifts immediately to the outer surface. Now, the uncharged belt again comes to collect more charge and follow the process again and again and the charge accumulates on the bigger spherical conductor.
But there is a limitation of the capacity of the spherical conductor to carry the charge.
It is given by capacitance $C$.
We know that $C=\dfrac{Q}{V}$
  If $Q$ is the charge in the conductor and \[V\] is the voltage due to that charge.
So, $V=\dfrac{Q}{4\pi {{\varepsilon }_{0}}k}\left[ \dfrac{b-a}{ab} \right]$
Where, $k$ is dielectric constant in the conductor for air it is nearly equals to $1$. $b,a$ are outer and inner radius of conductor respectively.
So, capacitance of the body is $\dfrac{4\pi {{\varepsilon }_{0}}ab}{b-a}$.
So, for increasing the capacity of the generator we need to increase the diameter of conductor and also thickness will be reduced.

Note: A Van de Graff generator terminal does not need to be sphere-shaped to work, and in fact, the optimum shape is a sphere with an inward curve around the hole where the belt enters. A rounded terminal minimizes the electric field around it, allowing greater potentials to be achieved without ionization of the air, or other dielectric gas, surrounding.