Figure above shows a closed Gaussian surface in the shape of a cube of edge length 3.0 m. There exists an electric field given by `vec(E) = [(2.0xx +4.0)i+ 8.0 j+ 3.0 k]N//C`, where x is in metres in the region is which it lies. The net charge in coulombs enclosed by the cube is equal to

Options

A. `-54 in_(0)`
B. `6 in_(0)`
C. `-6 in_(0)`
D. `54 in_(0)`

Answer

D

Explanation

`phi=intvec(E).dvec(s)`
Direction of field at x=-3m is along negative x axis. Area vector is alos along same direction.
`phi=6xx9=Q/(in_(0))`
`Q=54 in_(0)`
Components of electric field which are constant. Do not contribute in net flux in or out.
`q_("in")/(in_(0))=54rArr q_("in")=54 in_(0)`