1.

Theelectricfieldin a regions is givenby vec(E) = E_(0) (x)/(L) hat(i) . Findthechargecontainedinsidea cubical volume boundedbythe surfacex =0,x=L,y = 0,z = 0and z=L.

Answer»

SOLUTION :At x = 0,E = 0 andat `x = L , vec(E) = E_(0) hat(i)`
Thedirection of the field is alongthe X - AXIS ,so it will cross the yz-faceof thecube. Thefluxof thisfield .

`PHI =phi_("left face") + phi_("RIGHT face") = 0 + E_(0)L^(2) = E_(0)L^(2)`
By Gauss.s law ,`phi = (q)/(in_(0)) "" therefore q = in_(0) phi= in_(0)E_(0)L^(2)`


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