Van de Graaff Generator

Van de Graaff Generator

Q. With a neat sketch, explain the working of a Van-De-graff generator. What are the factors that limit the maximum output voltage obtained ?

• A Van de Graaff generator is a device that creates high electric potential.
• The Van de Graff generator was invented by Robert J. Van de Graaff, and American physicist (1901 - 1967).
• Van de Graaff generators can produce electric potentials up to many 10s of millions of volts. 
• Van de Graaff generators can be used to produce particle accelerators.
• We have been using a Van de Graaff generator in lecture demonstrations and we will continue to use it.

Working Principle of Van de Graaff Generator :

Figure A

• The Van de Graaff generator work by applying a positive charge to a non conducting moving belt using a corona discharge.
• The moving belt driven by an electric motor carries the charge up into a hollow metal sphere where the charge is taken from the belt by a pointed contact connected to the metal sphere.
• The charge that builds up on the metal sphere distributes itself uniformly around the outside of the sphere.
• For this particular Van de Graaff generator, a voltage limiter is used to keep the Van de Graaff generator from producing sparks larger than desired.
• Friction between acrylic roller and rubber belt.
• Lower comb sprays on negative charge by induction.
• Upper comb sprays positive charge to leave negative charge on dome.
• Millions of volts achievable in dry conditions.

Figure B

Figure C

Figure D

Figure E

Figure F

Figure G

Figure H

Figure I

Van de Graaf Generator :

• Rubber band steals electrons from glass.
• Glass becomes positively charged.
• Rubber band carries electrons downward.
• Positively charged glass continues to rotate.
• Wire "brush" steals electrons from rubber band.
• Positively charged glass steals electrons from upper brush.
• Sphere (or soda can) becomes positively charged to 20,000 volts.

Figure J

Power Required to move the Belt

• An insulated belt is moving with uniform velocity v in an electric field of strength E (x). Suppose the width of the belt is b and the charge density consider a length dx of the belt, the charge dq = σbdx
• The force experienced by this charge (or the force experienced by the belt) is given by,

dF = Edq = E  σbdx or F =  σb ∫Edx

Since the electric field is uniform, therefore,

F = σ bv

The power required to move the belt -

= Force x Velocity

= F v = abVv

Now, I = dq/dt = ob (dx/dt)

Therefore 1 = σ bv

Hence Power required to move the belt is

P = F v = σ bVv = VI

Advantages of Van de Graaff Generator :

• Very high voltages can be easily generated.
• Ripple free output.
• Precision and flexibility of control.

Disadvantages of Van de Graaff Generator :

• Low current output.
• Limitations on belt velocity due to its tendency for vibration. The vibrations may make it difficult to have an accurate grading of electric fields.

Applications of Van de Graaff Generator :

• The beam of these charged accelerated particles is used to trigger the nuclear reaction.
• Accelerated particle beams are used to break atoms for various experiments in physics.
• In medicine, such beams are used to treat cancer.