Figure above shows a closed Gaussian surface in the space of a cube of edge length 3.0m. There exists an electric field given by `vec E= [(2.0x+4.0)i +8.0j +3.0k]N//C`, where x is in metres, in the region in which it lies. The net charge in coulumbs 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 = int vec(E).d vec(s)`
Direction of field at x = -3 m is along negative x axis. Area vector is also along same direction
`phi = 6 xx 9 = (Q)/(epsilon_(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))=54 rArr q_("in") = 54 in_(0)`