# PP10 - Texas State University—San Marcos Ingram School of...

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Unformatted text preview: Texas State University—San Marcos Ingram School of Engineering EE3340: Fields and Waves So L. o T L o U Q Practice Problem 10: Van de Graaff Generator NAME: DATE: The only electrostatic generator still in use today is the Van de Graaff generator, named after Robert Van de Graaff, who invented it in the 19305. It consists of a insulating belt that travels between two pulleys at either end of a long insulated column: A high—voltage DC source sprays charge (negative in this example) onto the belt at the base. A large spherical conductor is mounted at the top of the column. When the charge reaches the upper pulley inside the sphere, it jumps off through a brush electrode to the sphere and collects there. For the purposes of this problem, you can assume the sphere is a perfect isolated sphere in space. 1. Calculate the electric ﬁeld magnitude IE,| at the surface of the sphere, as a function of the sphere radius r (meters) and the potential V (volts). H'r‘e , q-te hr ‘ @l Vw :Lo. 2...)“. [Orv/“3 : m a.) v... - (”nah m. m _ , ”h 5‘ E”:[}' L I ‘W ‘o ' = ‘euLs.%st'(I"‘r=/~)(1.),m):. 2 S S e l‘ : if” . 5 ”9 "° ”(“99 v - >— 2. Typical physics-lab generators have a sphere with a radius of about 20 cm, while one __ of the largest open-air VdeG generators ever made (still in operation at the Boston “ ' .l ‘17 Museum of Science) uses a sphere with a radius of 2.3 m. If the voltage limit is caused by air breaking down at a surface ﬁeld of 3 MV m“, calculate the maximum theoretical voltage for (a) a 20—cm—radius generator and (b) a 2.3—m—radius generator. What is the energy stored in the (b) generator at maximum voltage (in joules)? [@C‘erk V6‘Pg195 i‘owr 1‘7, Wee NV\W(MQ/Ko) ...
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