Question

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 x 10³ Nm²/C.
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or why not?

Answer 1

(a) Φ = \(\frac{\mathrm{q}}{\varepsilon_{0}}\)
q = Φ x \(\varepsilon_{0}\)
= 8 x 10³ x 8.85 x 10^-12
= 0.07 μC

(b) If the net outward flux through the surface of the box is zero, it cannot be concluded that there is no charge inside the box. There may be an equal amount of positive and negative charges inside the box. Therefore, if the net outward flux is zero, we cannot conclude that the charge inside the box is zero. One can only say that the net charge inside the box is zero.