Question

Draw a well labelled diagram of Van de Graff generator. State its working principle to show how by introducing a small charge sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

Answer 1

Hint: In this question we have been asked to state the working principle of Van de Graff generator. Also, we have to show that by introducing a small charge sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. Therefore, to answer this question, we shall first discuss the construction and working of the given instrument with the help of a labelled diagram.

Complete answer:
Van de Graff generator is an electrical device that uses a belt moving with the help of a motor to collect the electric charge and spread it across the outer surface. This creates a very high electric potential. It is based on the principle that like negative charges repel each other and spread out to the outer surface of the sphere. The construction of the Van de Graff generator is as shown in the figure below.

                 

The Van de Graff is a series of combinations that allows the charge to flow in only one direction. Also, the Van de Graff is able to accelerate only the charged particles. These two factors are the limitations of the instrument.
Now, let the charge on inner radius r be q and the charge on outer radius R be Q
Therefore, potential on the inner sphere will be given by,
\[V(r)=\dfrac{1}{4\pi {{\varepsilon }_{o}}}\left( \dfrac{Q}{R}+\dfrac{q}{r} \right)\] …………………… (1)
Similarly, the potential outer sphere,
\[V(R)=\dfrac{1}{4\pi {{\varepsilon }_{o}}}\left( \dfrac{Q}{R}+\dfrac{q}{r} \right)\] …………………….. (2)
Now subtracting (2) from (1)
\[V(r)-V(R)=\dfrac{q}{4\pi {{\varepsilon }_{o}}}\left( \dfrac{1}{r}-\dfrac{1}{R} \right)\]
The above shows that the outer sphere will always remain at higher potential. After connecting the two spheres, charge will start flowing between the two. This will allow more charge to accumulate on the outer sphere.
The Van de Graff is used to produce high voltage. It is also used as an electro-static accelerator for scientific experiments.

Note:
A Van de Graff pulls electrons from the earth. These electrons are stored on the outer sphere on the generator. These electrons repel each other and in doing so spread as far as possible. If you touch a Van de Graff generator the hair on your head stands up straight. This happens because the electrons now spread from the outer sphere to the hair follicles and try to stay apart, which causes the hair to stand up.