# T03 - TUTORIAL 3 1 a z 2 cos a 4z sin a z mC/m 2 using two...

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TUTORIAL 3 1. If D = 2 z 2 sin " 2 a # + z 2 cos 2 a + 4 z sin 2 a z mC/m 2 , using two different methods, find the total charge enclosed by the object defined by " 2 # z # 1 , 1 " " 4 , 0 " " \$ . 2. Given that D = 2 z cos 2 a \$ z sin cos a + 2 cos 2 a z C/m 2 , calculate the electric flux through the following surfaces of the cylinder: (a) Surface = 3, 0 # z # 5 ; (b) Surface z = 0, 0 " " 3 ; (c) Surface z = 5, 0 " " 3 ; (d) Calculate the charge enclosed by the whole cylinder = 3, 0 # z # 5 . 3. (SADIKU p. 177, practice exercise 5.5) A thin rod of cross section A extends along the x -axis from x =0 to x = L . The polarization of the rod is along its length and is given by P x = ax 2 + b . Calculate the volume polarization charge density bound and surface polarization charge densities Sb at each end. Hence, show explicitly that the total bound charge vanishes for this particular case. 4. (after Cheng p. 111, Example 3-12) A positive point charge Q is at the centre of a spherical dielectric shell of inner radius i R and outer radius o R . The dielectric constant of the shell is r ! . Determine expressions for the electric field intensity E , the polarisation P , the electric flux density D , the surface bound charge density Sb and the volume bound charge density bound versus radial distance R . Plot the expressions for E , P and D . Under what conditions will bound be non-zero?

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T03 - TUTORIAL 3 1 a z 2 cos a 4z sin a z mC/m 2 using two...

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