An electron cloud has a shape of an infinite cylinder, with the radius a and the...
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An electron cloud has a shape of an infinite cylinder, with the radius a and the space charge density po C/m (assumed constant in this problem). The center of the cloud is at the distance h (> a) above a large, conducting plane (assumed infinitely large in this problem). a) Formulate a potential problem, including equation and boundary condition such that the electric potential and field above the conducting plane can be determined from the solution of the problem b) Show that the electric potential above the plane is given the expression below Hint: use method of mirror images. Poa² In (*:/R,).R1 > a, R %3D 280 Poa? R1 where R, and R2 are the distances to the centers of the real and image cylinders respectively. c) What is the largest induced surface charge density on the conducting plane? An electron cloud has a shape of an infinite cylinder, with the radius a and the space charge density po C/m (assumed constant in this problem). The center of the cloud is at the distance h (> a) above a large, conducting plane (assumed infinitely large in this problem). a) Formulate a potential problem, including equation and boundary condition such that the electric potential and field above the conducting plane can be determined from the solution of the problem b) Show that the electric potential above the plane is given the expression below Hint: use method of mirror images. Poa² In (*:/R,).R1 > a, R %3D 280 Poa? R1 where R, and R2 are the distances to the centers of the real and image cylinders respectively. c) What is the largest induced surface charge density on the conducting plane?
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Related Book For
Principles of heat transfer
ISBN: 978-0495667704
7th Edition
Authors: Frank Kreith, Raj M. Manglik, Mark S. Bohn
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