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HW3_solutions

# HW3_solutions - EEE241 Fundamentals of Electromagnetics...

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EEE241 – Fundamentals of Electromagnetics – Spring 2007 Solutions to Homework 3 P3.5: Two point charges, 12 Q and Q are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q and Q such that the total force on a test charge at the point P (-1,1,0) will have (a) no x -component and (b) no y -component. 11 22 2; 5 3; 1 0 xy QP a a a a =− = + = rr 2 2 33 1 4 P o QQP QQP E πε ⎡⎤ ⎢⎥ =+ ⎣⎦ r = () 3/2 1 23 45 1 0 o QQ aa −−+ −+ r r (a) no x -component 1 2 3 0 51 0 42 Q Q −= = (b) no y -component 1 2 1 0 0 Q Q += = P3.10: Assuming that the electric field intensity is ( ) 100 / x Ea x Vm = r r , find the total electric charge contained inside (a) a cubical volume 100 (mm) on a side centered symmetrically at the origin (b) a cylindrical volume around the z-axis having a radius 50 (mm) and a height 100 (mm) centered at the origin. (a) Use Gauss’s law and Cartesian coordinates. Cube has six sides of area (100mm) 2 . E r is normal to the two sides at 50 x mm , where 5 x nx E a and a a = ±= ± r r , and only these two sides contribute to . E ds r r . 32 (100 10 ) 0.01 x x ds a a × r

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13 .2 5 0 . 0 1 0.1 8.854 10 o o Q Eds QC ε =×× = ==× r r (b) Convert to cylindrical coordinates. cos sin ; cos xr aa a x r φ φφ =− = rr r 2 100 cos 100 sin cos r Ea r a r r 22 0.05 2 2 0.05 0 13 . 100 cos . 0.25 cos 0.025 0.025 6.44 10 r o dS a r d dz EdS r d dz d π φπ πε = = == × ∫∫ r r r r r r ±
EEE 241 Solution to Assignment #3 P.3-11 A spherical distribution of charge ρ = ρ 0 b 1 ( R 2 /b 2 )B exists in the region 0 R b . This charge distribution is concentrically surrounded by a conducting shell with inner radius R i ( > b ) and outer radius R o . Determine E everywhere.

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HW3_solutions - EEE241 Fundamentals of Electromagnetics...

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