[...]... density (which now depends on r) to obtain mutually consistent values Download free ebooks at bookboon.com 24 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples Example 1.10 Figure 1.13 shows a simplified form for the deflection plates for a low current electron beam Given that the electron beam is launched from an electrode (the cathode) at a potential of -2000V and passes... ratio of the electron The time taken for an electron to pass along the length of the plates (L) is then t L vx 1.89 ns (1.47) The equation of motion in the y direction for an electron is m d2y dt2 qE y (1.48) Download free ebooks at bookboon.com 25 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples where q is the magnitude of the electronic charge The transverse acceleration... contains the standard formula and the green areas use formulae which assume symmetry at the boundaries Download free ebooks at bookboon.com 33 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples The method can be applied to more complicated problems including those with curved electrodes which do not fit the mesh and three-dimensional problems Further information can be found... Download free ebooks at bookboon.com 11 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples b) - + + - Fig 1.3 Image charges for planes intersecting at 90° c) When the planes are at 60° to each other five image charges are equally spaced on a circle as shown in fig 1.4 + + - + Fig 1.4 Image charges for planes intersecting at 60° d) No The method can only be used when... bookboon.com 13 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples Solution For most practical purposes the properties of air are indistinguishable from vacuum From the symmetry of the problem we note that the electric field must everywhere be radial The field between the conducting cylinders is identical to that of a long, uniform, line charge q placed along the axis of... can be integrated by writing 1 V 4 dx 4J 2 0 dx (1.57) Performing the integration we get 4 3 3 4J V4 0 x C (1.58) 2 Now V = 0 when x = 0 and therefore the constant of integration C is zero At the anode V = Va and x = d so that Download free ebooks at bookboon.com 28 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples 3 Va2 9 4 d2 0 2 J (1.59) as required The total current... space Electromagnetism for Electronic Engineers – Examples Fig 1.17 The finite difference solution for one quadrant of the problem: The initial stages The process is continued until no further changes are observed in the figures to the accuracy required The final result is shown in fig 1.18 Evidently the accuracy could be improved by using a finer mesh Fig 1.18 The finite difference solution for one... free space Electromagnetism for Electronic Engineers – Examples The electrode potentials are entered into the cells corresponding to the electrodes and the formula in Equation [1.30] is entered into all the other cells It is convenient to take the electrode potentials as 0 and 100 to reduce the number of digits displayed When symmetry has been used to reduce the size of the problem the formulae in... should be renewable, too We are therefore looking for enthusiastic new colleagues with plenty of ideas who want to join RWE in changing the world Visit us online to find out what we are offering and how we are working together to ensure the energy of the future Download free ebooks at bookboon.com 14 1 Electrostatics in free space Electromagnetism for Electronic Engineers – Examples Let the radial component... E The integral form of Gauss’ theorem (all materials) D dS dv [2.5] The differential form of Gauss’ theorem (all materials) [2.6] D Boundary conditions The tangential component of E is continuous at a boundary The normal component of D is continuous at a boundary Download free ebooks at bookboon.com 35 2 Dielectric materials and capicitance Electromagnetism for Electronic Engineers – Examples The definition . Carter Electromagnetism for Electronic Engineers – Examples Download free ebooks at bookboon.com 3 Electromagnetism for Electronic Engineers – Examples ©. prepared for tomorrow’s management challenges and apply today. Download free ebooks at bookboon.com Electromagnetism for Electronic Engineers – Examples