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EXAM1_Q_2 - f{B Let us assume that the electric field is...

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Unformatted text preview: f. {B Let us assume that the electric field is given in component form l// . E = Eri + Eyi We are told that Ex is’proportlonal to y , E1 = ay and all we know is that Ey= O wherever x= 0. Can we uniquely determine Ev? . "5‘“. 1—.— \/.‘ j" The electrostatic potential in a region of space is given as \ (fi+xw+f—awl V= V0 a2 Find all points Where the electric field vanishes, as well as all points where it is directed along the x-direction or along the y-clirection. KKA .- 5 3 The electric field in a region of space has the form 2v 1 E0 / E; ;-(x — y) ' a 4 —E Eu = a 0 (x + y) E: = O (”_, .— Calculate the electrostatic potential V(x,y,z) and check that ‘35:? weighs satisfied for any rectangular loop parallel to the coordinate axis. 1 Gil: Consider the arrangement of three point charges Q1, kQ1(k > O), and Q2, as / shown in Fig. 2.40, Where Q1 and le are fixed and Q2 is constrained to move‘on . the semicircle. (a) Find the value of a in terms of k for which Q2 is in equilibrium: (b) Find the numerical value of a: for k = 8. ‘ - I --. in HGUREZAO \/QE:; Medium 1, comprising the region r‘ < a in spherical coordinates, is a perfect di- - electric of permittivity 81, Whereas medium 2, comprising the regionr > a in spherical coordinates, is free space. The electric field intensities in the two media are given by E1 = E01(cos 6 a, —- sin 6 as) . a3 [13 = + n _ _ _ ' E2 E02[<1 27;) cos 0 a, (1 41/5) 5111 9 219] respectively. Find 21. , 12%} A boundary sepfiates free space from a perfect dielectric medium. At a point on ‘ the boundary, the electric field intensity on the free space side is E1 =1 EGG-a: + 2213, + Sax), Whereas on the dielectric side, it is E2 = 3Eo(ax + a2), WhereEO is a constant. Find the permittivity of the dielectric medium; ...
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