The figure shows a cube whose sides are all 5cm long. Over the entire left-hand side of the cube is a uniform electric field E1=7500 N/C which is entering the cube at 20 degrees below the x axis. Over the right-handed side is a uniform electric field E2=4500 N/C which is leaving the cube at 60 degrees below the x axis.

Question

a) Assuming that no other electric field lines cross the surface of the cube, determine the net charge contained within.
b) Is the electric field produced only by the charge within the cube, or is the field also due to charges outside? How can you tell?

Answer 1

a. Gauss' law. E dot Area=chargeenclosed

b. Is there a component of E on each side the same? If so, that E is generated outside.

For instance, on the left side, E dot area=7500*25cos20=1.76E5
one the right side, leaving 4500*25cos60=1.07E5

So the meaning of this is that there is a net flux entering, which means a charge is enclosed, and the remainder of E going to the right is caused by something exterior to the cube.

Answer 2

Is the magnitude the same as the net charge for a?

Answer 3

yes, the net charge comes from E dot A