Electric flux through a planar loop with charges on either side

[Theelectricchild]

This problem is quite annoying considering I see it testing us in knowing when you can and cannot apply Gauss Law.

The loop shown here

http://uploader.clausercorp.com/uploaded/Loops.JPG

(I tried to draw it best i could) has an area of A, held to the right of a positive point charge +Q. The surface bounded by the loop is a plane--- so the area vector (I didnt draw) would be pointing perpendicular to the "plane" that is inside that loop, to the right.

Would the electric field flux thru the loop due to the charge be positive negative or zero?

At first I would say yes, considering the field lines are coming out of +Q and are "flowing" thru the plane. IE: E dot A would be positive since the Area vector I drew would be facing the same direction as the x components of the field lines--- correct?

But then I wonder if its possible to use Gauss Law at all since the charge isn't enclosed by the surface--- or am I getting my definition mixed up?

Also say a +2Q charge is placed to the right of the loop, and the +Q charge was still to the left. Would the flux change?

i understand there would be more field lines coming out of the + 2Q charge, but since i drew my area vector pointing to the right of the loop--- would the +2Q charge allow for the net flux due to both +Q and +2Q be negative?

And another situtation is when the +2Q is negative instead--- IE -2Q. Would that change anything?

THanks for your help--- conceptually i find it difficult...

 

[Doc Al]

At first I would say yes, considering the field lines are coming out of +Q and are "flowing" thru the plane. IE: E dot A would be positive since the Area vector I drew would be facing the same direction as the x components of the field lines--- correct?

Right.

But then I wonder if its possible to use Gauss Law at all since the charge isn't enclosed by the surface--- or am I getting my definition mixed up?

Why are you bringing up Gauss's law?

Also say a +2Q charge is placed to the right of the loop, and the +Q charge was still to the left. Would the flux change?

The total flux through the loop will be the sum of the fluxes from each charge. So what do you think?

i understand there would be more field lines coming out of the + 2Q charge, but since i drew my area vector pointing to the right of the loop--- would the +2Q charge allow for the net flux due to both +Q and +2Q be negative?

Yep.

And another situtation is when the +2Q is negative instead--- IE -2Q. Would that change anything?

What do you think? Does the flux depend on the direction of the field?

 

[M98Ranger]

It seems like you have a good understanding of the concepts involved in this problem, so let's work through it together. First, let's address the use of Gauss' Law. Gauss' Law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε0). In this problem, the surface bounded by the loop is not closed, so we cannot directly apply Gauss' Law. However, we can still use the concept of electric flux to analyze the situation.

Now, let's consider the situation with just the +Q charge. As you correctly stated, the electric field lines will be coming out of the +Q charge and passing through the plane defined by the loop. Since the area vector is pointing in the same direction as the electric field lines, the electric flux through the loop will be positive.

Next, let's consider the situation with both the +Q and +2Q charges. In this case, the electric field lines from both charges will be passing through the loop. Since the area vector is still pointing in the same direction, the electric flux through the loop will still be positive. The presence of the +2Q charge does not change the direction of the electric field lines passing through the loop.

Now, let's consider the situation with a -2Q charge instead of a +2Q charge. In this case, the electric field lines will be directed towards the -2Q charge, and therefore, the electric flux through the loop will be negative. This is because the area vector is still pointing in the same direction, but the electric field lines are now in the opposite direction.

In summary, the electric flux through the loop will be positive when there is a positive charge present, and negative when there is a negative charge present. The presence of multiple charges can affect the magnitude of the electric flux, but not the direction. I hope this helps clarify the concept for you. Keep practicing and you will become more comfortable with these types of problems. Good luck!