## Electric Field & Flux, A loop & Charge

Hey everyone. Having a bit of trouble with a 4-part question. So I thought I'd post here, if someone could check the first 3 parts and perhaps help me with the last part, I'd really appreciate any feedback! Thank you so much! :)

1. The problem statement, all variables and given/known data

a) A circular loop is held to the left of a positive point charge (+Q). (part i. asked us to draw an Area vector and the electric field lines). Is the electric flux through the loop due to the charge positive, negative, or zero? Explain.

b) A positive charge with twice the value of the initial charge (so +2Q) is now place to the left of the loop. Both charges are the same distance from the loop and are placed along the axis of the loop. Is the net electric Flux through the loop positive, negative, or zero? Explain your reasoning. Use the same area vector you used in part a.

c) Suppose the new charge located to the left of the loop had been negative instead of positive. How, if at all, would your answer to part b change? Explain.

d) Do you agree or disagree with the following student:

"I can calculate the flux through the loop by finding the electric field at the center of the loop and then taking the dot product of that value with my area vector for the loop"

If you disagree, is the absolute value of the flux through the loop that the student would calculate greater than, less than, or equal to the correct value? Explain

2. Relevant equations

Electric Flux = E (dot) Area = EA cos (theta)

3. The attempt at a solution

a) I drew the area vector perpendicular to the plane of the circular loop, pointing to the left. And then I said the electric field lines are coming out of +Q and passing through the loop. So E (dot) A would be positive, because Ex and A are both pointing in the same direction ( to the left), and the Ey components all cancel out.

b) I said in this case, there are more Ex lines from the +2Q charge becuase it has a great magnitude, so the net Ex is to the right (because the +2Q charges electric field lines point to the right). Since I had made my area vector point to the left, the directions of the Area vector and the net Ex are in opposite directions, so the net electric flux through the loop is negative.

c) I said that the Ex due to -2Q would have direction to the left, because it is negative, so the net Ex would be to the left. And since my area vector is to the left, and the net electric field Ex is to the left, the electric flux would have been positive not negative had it been -2Q

and finally, for part d), I'm not really understanding what the student is saying. Could someone point me in the right direction? Thank you!
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 For part a I think the area vector can point either way, it just needs to be perpendicular to the surface? For part b and c, same as above? For part d, if the size of the loop were very small compared with the distance between the loop and the charge then you will get a answer close by the method suggested in part d. As always, I hope any errors with the above are pointed out.
 Yes, I see how Area vector could be in either direction. If I had chosen it to go to the right, then for part a) my answer would be negative, and part b) positive. ? Is the reasoning for part c correct? I guess I just want to make sure that that's how it works! Also, thanks for the input with part d! As always, anyone else's additional input would also help! Thanks!