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Question Number 82647 by Learner-123 last updated on 23/Feb/20

In the rectangular region, −2<x<2,  −3<y<3, the surface charge density  is given as ρ_s =(x^2 +y^2 +1)^(3/2) . If no other  charge is present, find E at P(0,0,1).

$${In}\:{the}\:{rectangular}\:{region},\:−\mathrm{2}<{x}<\mathrm{2}, \\ $$ $$−\mathrm{3}<{y}<\mathrm{3},\:{the}\:{surface}\:{charge}\:{density} \\ $$ $${is}\:{given}\:{as}\:\rho_{{s}} =\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} .\:{If}\:{no}\:{other} \\ $$ $${charge}\:{is}\:{present},\:{find}\:{E}\:{at}\:{P}\left(\mathrm{0},\mathrm{0},\mathrm{1}\right). \\ $$

Commented byLearner-123 last updated on 23/Feb/20

Can this Q. be done with the help of   symmetry?

$${Can}\:{this}\:{Q}.\:{be}\:{done}\:{with}\:{the}\:{help}\:{of}\: \\ $$ $${symmetry}? \\ $$

Commented byLearner-123 last updated on 26/Feb/20

??

$$?? \\ $$

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