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…………..

Explanation

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))