Question

An electric field is given by `vec(E)=4hat(i)+3(y^(2)+2)hat(j)` pierces gaussian cube of side 1 m placed at origin such that one of its corners is at origin & rest of sides are along positive side of coordinate axis. If the magnitude of net charge enclosed is n `varepsilon_(0)` then n (in SI units) will be equal to

Answer 1

Correct Answer - `0003`
Along z axis `vec(E) . D vec(A) =0`
Along x axis `vec(E) =const`
`:.phi_(x)=0`
for y=0
`int vec(E) . Dvec(A)= int 3(0+2)hat(j)dA (-hat(j))=6intdA =-6`
y=1
`intvec(E) . Dvec(A) = int3(1+2)hat(j).dA(hat(j))=9intdA=9`
`:.phi_(net)=+3in_(0)`