Q. 174.3( 57 Votes )

# 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 × 10^{3} Nm^{2}/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 :

Given:

(a) Φ = 8.0 × 10^{3} Nm^{2}C^{-1}

Let net charge inside the box = q

We know that,

Flux, Φ = q/ε_{0} ..(1)

Where, q = net charged enclosed

ε_{0} = permittivity of free space

ε_{0} = 8.85 × 10^{-12}N^{-1} m^{-2}C^{2}

Plugging values of Φ and ε_{0} in equation (1) we get,

q = Φ × ε_{0}

⇒ q = 8.0 × 10^{3} Nm^{2}C^{-1} × 8.85 × 10^{-12}N^{-1}C^{2}m^{-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.

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