question_answer

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of box is \[8\times {{10}^{3}}N{{m}^{2}}{{C}^{-1}}.\]

(i) What is the net charge inside the box?

(ii) If the net outward flux through the surface of the box was zero, what can you conclude about the presence of charges inside the box.

Answer:

(i) Given, electric flux,     \[\phi =8\times {{10}^{3}}N{{m}^{2}}{{C}^{-1}}\] From Gauss? theorem,     \[\phi =\frac{1}{{{\varepsilon }_{0}}}\cdot q\] \[\therefore \] Net charge enclosed,             \[q={{\varepsilon }_{0}}\phi =8.85\times {{10}^{-12}}\times 8\times {{10}^{3}}\]             \[=70.8\times {{10}^{-9}}C=70.8\,nC\]

(ii) If the net outward flux is zero, it indicates that the net charge enclosed in the black box is zero. The conclusion is either.

(a) There is no charge inside the box.

(b) There may be different types of charges in the box such that the algebraic sum of charges inside the box is zero.