# Van de Graaff Generator

## Van de Graaff Generator

American Physicist, Robert J. Van de Graaff was the person behind this invention. A Van de Graaff generator is an electrostatic generator and it is used to generate high voltages of a few millions of volts.

What is Van de Graaff generator?

Van de Graaff generator is a device which is used for building up high potential difference of the order of 10⁴ volt. Such charges particles like deuteron, proton, ions etc. can be accelerated by using this generator.

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. The electric filed inside the sphere is zero and the outside the sphere is due to the charge Q at the centre of the sphere. So, the potential outside is that of a point charge and inside it is constant.

Potential inside conducting spherical shell of radius R carrying charge Q is constant.

$$V=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{R}$$.

Now place a small sphere at the centre of the large one such that the radius of the smaller sphere is r and the charge over its surface is q. At the surface of the small sphere:

$${{V}_{{{r}_{1}}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{r}$$.

At the large spherical shell of radius R:

$${{V}_{{{r}_{2}}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{R}$$.

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 is:

$${{V}_{R}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{R}+\frac{Q}{R} \right)$$.

$${{V}_{r}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}+\frac{Q}{R} \right)$$.

$${{V}_{R}}-{{V}_{r}}=\frac{q}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}+\frac{Q}{R} \right)$$.

Uses of Van de Graaff generator:

1. It is used to create a high potential of a range of few million volts.

2. It is used to study collision experiments in physics.

3. It is used to accelerate projectiles like proton, deuterons etc. which hit the target with large kinetic energy and bring about artificial transmutation.