a) Consider a charge uniformly distributed (with constant density P.) across an infinite straight line along the z-axis,
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a) Consider a charge uniformly distributed (with constant density P.) across an infinite straight line along the z-axis, as shown in Fig 3.1. +Z da N Fig 3.1: Calculating the electric field intensity at point P fixed at a distance r from the line. 1) What is the coordinate system most appropriate to tackle this kind of question? Why?
ii) Given that we wish to determine the electric field intensity at a certain point P from the line, write an initial expression for the differential electric Page 6 of 8 ELECTROMAGNETIC THEORY (ASE2103) SITEJAP 2014-2015 S2 field intensity dĒ in terms ofāg, where ā, is the unit vector that points from the differential charge dQ to the point P, both separated by a distance R (not shown in Fig 3.1). (2 marks)
iii) Show that dĒ can be reduced to: dĒ p.dz 4πε, 2+: rā, -zā. (6 marks) iv) One of the two unit vectors of the result of ii) can be eliminated. Which one is it? Why? (1 + 1 marks) v) Using the results below: rdx R= Vax' +bx+c where R 4ax + 2b 4ac-b2 R Further show that Ē can be finalized as E P 2πε,r PLā, (6 marks) iv) What you observe in terms of dependency on the distance when comparing the electric field intensity due to a point charge to that of line charge.