Question

Question 1.17: 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 N m 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?

Class 12 - Physics - Electric Charges And Fields Electric Charges And Fields Page-47

Answer 1

a) Ф = q÷∈o

q = Ф×∈o = 8×10^3 × 8.85×10^-12 = 7.08×10^-8 C

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b) No, because net flux depends upon the net charge of the body. If net flux through a body is zero it means that the net charge of the body is zero. It doesnt mean that the body doesnt contain any charge , the body might be carrying equal amount of positive and negative charges.

Answer 2

Answer:

a) The net charge inside the box is $7.08*10^{-8} C$

b) There are is no net charge inside the box

Gauss's law: It states that the net outward flux across any closed surface is proportional to the charge enclosed by the surface

Explanation:

a)Given that the net outward flux Ф = $8 * 10^{3} Nm^{2} /C$.

From Gauss's law, we obtain that Ф = $\frac{q}{E_{0} }$ where $E_{0}$ is the permittivity of the free space.

Now the net charge equals to $8 * 10^{3} Nm^{2} /C * 8.85*10^{-12}$ C.

  q = $7.08*10^{-8} C$

b) Given that the net outward flux is zero. So from Gauss's law, we can say that the net charge enclosed is zero.