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 × 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?
Given:
(a) Φ = 8.0 × 103 Nm2C-1
Let net charge inside the box = q
We know that,
Flux, Φ = q/ε0 ..(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Plugging values of Φ and ε0 in equation (1) we get,
q = Φ × ε0
⇒ q = 8.0 × 103 Nm2C-1 × 8.85 × 10-12N-1C2m-2
⇒ q = 7.08 × 10-8 C
Hence, the net charge inside the box is 0.07 μC.
b) No, we cannot conclude that the body doesn’t have any charge. The flux is due to the Net charge of the body. There may still be equal amount of positive and negative charges. So, it is not necessary that if flux is zero then there will be no charges.