By A. J. Baden Fuller
Labored Examples in Engineering box idea is a manufactured from a lecture direction given by way of the writer to first-year scholars within the division of Engineering within the collage of Leicester. The publication offers a precis of box conception including loads of labored examples and recommendations to all difficulties given within the author's different e-book, Engineering box conception.
The 14 chapters of this booklet are equipped into components. half I specializes in the concept that of flux together with electrical flux. This half additionally tackles the appliance of the speculation in gravitation, perfect fluid circulation, and magnetism. half II bargains with the concept that of capability together with electric power, in addition to the functions of the speculation to gravitation, electrical conduction, fluid stream via permeable media, conductive warmth move, excellent fluid move, and magnetism.
This fabric should be important to scholars who've hassle with the issues provided within the author's different e-book, or who want additional labored examples and extra difficulties to unravel.
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Extra resources for Worked Examples in Engineering Field Theory. Applied Electricity and Electronics Division
Sample text
17. Find the electric field intensity at a distance of 10 m away from a long, straight conductor which carries an electric charge density of 22-2 yC/m. 18. Find a general expression for the flux density inside and outside an infinitely long straight tube having an inner radius a and outer radius b whose material has a uniform charge density p. , and 3 p = 0·1 yC/m , find the flux density at a distance of 8 mm and 100 mm from the centre of the tube. 19. An infinite plane sheet has a uniform charge density of 10 yC/m2.
The geometry for obtaining the flux function of the combination is shown in Fig. 4, where the flux function is seen to be Ψ = Ψι + Ψ2 ïî , e · -3q/4=q/4l Fig. 3. The flux function values due to the combined field of a line source and a line sink, of strength ±q C/m. Fig. 4. Illustrating a mathematica! expression for the flux function values due to the combined field of a line source and a line sink. 10) Flux Function 39 The locus of the points having the angle a constant v/ill be the segment of a circle passing through the points A and B.
8 (page 26). Therefore sin ~ l Vi area = 2i\r2 Therefore sin Θ dQ = liw1 (- — + 1) = 0*134 χ 2π^ 2 . f solid angle = 0-134 χ 2π = 0-844 sr, ^" 6 * ° · 1 3 4 * ^ = 6-7 x 1 0 - C = 67 nC. 12. From Gauss's law, as there is no charge enclosed within the insulating sphere, there is no net flux flowing into or out of the surface of the sphere. The answer is zero. 13. 14. EY = 1Q ~8 x 36TT X 1Q9 = 9-0 x 10 5 V/m = 900 kV/m, 4π x IO"4 IO"8 χ 36π χ IO9 = 88 V/m. 4π χ 1-02 The force on one end charge is given from Coulomb's law, 2-0 x 10~ 6 x 1-0 x 1 0 1 6 x 36π χ IO 9 + 2-0 χ IO"6 χ 2-0 χ IO"6 χ 36π χ 1Q9 4π χ 10" 2 4π χ 4 χ 10" 2 = 9 χ IO'1 (-2-0 + 1·0) = -9-0 χ IO"1 N = -0-9 Ν.
