Answer to Question #234977 in Physics for Soriano

Question

A butterfly net hangs from a circular loop of diameter 430mm. You hold the loop horizontally in a region where electric field is 149 N/C

What is the electric Flux through the net?

Does Flux increase or decrease if you rotate loop so that it lies vertical in a plane?

Answer 1

By definition, the flux is given as follows:

$$\Phi = ES\cos\theta$$

where $E = 149N/C$ is the field (should be constat), $S = \dfrac{\pi d^2}{4}$ is the surface area (in this case circle with diameter $d = 430mm = 0.43m$), and $\theta$ is the angle (from the normal to the surface) between field and surface. In the first case $\theta = 0\degree$, since the net is held horizontaly.

Thus, obtain:

$$\Phi = ES\cos\theta = \dfrac{\pi Ed^2}{4} \approx 21.6\dfrac{Nm^2}{C}$$

In the second case the angle become $\theta = 90\degree$, then $\cos\theta = 0$ and the flux is 0.

Answer. 1) $21.6\dfrac{Nm^2}{C}$, 2) .