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An electric field prevailing in a region depends only on x and y coordinates according to an equation vecE = b(xhati + yhatj)/(x^(2) + y^(2))where & is a constant. Flux passing through a sphere of radius r whose centre is on the origin of the coordinate system is………….. |
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Answer» SOLUTION :As shown in the fig. `hatr`, is the UNIT VECTOR in the direction of `vecr`. `hatr = vecr/r = (XHATI + yhatj + zhatk)/r`………(i) Now, `vecE = b(xhati + yhatj)/(x^(2) + y^(2))` is given: For flux, applying Gauss.s LAW, `vecE.dveca = b(xhati + yhatj)/(x^(2) + y^(2)).((xhati+yhatj +zhatk)da)/r` `=b/r da` `therefore intvecE. dveca = b/r int da = b/r. 4pir^(2) = 4pibr`........(ii) But, `phi = intvecE.dveca``[therefore intda = 4pir^(2)]` `therefore phi = 4pibr` [From eq. (ii)) |
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