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EKT 241: ELECTROMAGNETIC THEORY SEM 2 2009/2010 TUTORIAL 2 – ANSWER Question 1 1. Find the total charge on a circular disk defined by r a and z 0 if s s 0 r 2 (C/m 2 ) where s 0 is a constant. The unit of r is in meter. Solution Q a r 0 2 0 s 0 0 2 2s 0 s 0 r 2 rdrd a 0 4 a r 4 0 a4 2s 0 4 a 4 s 0 C 2 r 3 dr Question 2 Find the total charge Q using Gauss’s law for a cylinder of height 3 m and radius 2 m, given the volume charge density V 2r sin (nC/m 3 ) . Solution Q 2r sin dV V 2 2 3 r 0 0 z 0 2 2r sin rdrd dz 2 3 0 0 2r 2 dr sin d dz 0 2 2r 3 2 3 - cos 0 z 0 3 0 0C Question 3 An infinite sheet of charge with uniform surface charge density ρs is located at z = 0 (x-y) plane and another infinite sheet with density - ρs is located at z = 2m, both in free space. Determine E in all regions. Solution The equation of E for infinite sheet of charge: For the sheet at z = o Question 4 Determine the electric potential at the origin in free space due to four charges of 20 C each located at the corners of a square in the x-y plane and whose center is at origin. The square has sides of 2 m each. Solution The potential due to ONE point charge Q : P2 V E dl (V) P1 R - Qr ˆ (rˆdr ) 2 0 4 r 0 r Q 40 r 0 Q 40 r