Understanding Gauss's Law: Solving with Correct Sign and Direction

[MitsuShai]

I know what formula you need to solve this problem (the attachment), but I'm having trouble with understanding the signs and direction of points A,B, and C.
I know that the lines go towards the negative and away from the positive, but I'm still not seeing the correct signs.

For instance I know that the charge on the charge density 1 near point A is negative and so the field lines go towards the left, which is way the charge density of 1 is negative.

Let's say for point B, for example, the charge density of 3 is going towards the left, so in my mind it should be negative and the charge density of 2 is going towards the right, so it should be positive, but I looked on the answer sheet and it's the other way around. I'm not understanding this.

 

[gneill]

Perhaps in the answer sheet they were summing the contributions to the field from both sides of each plastic sheet.

In the case of the left hand sheet, it has a charge density of -6.00 μC/m^2 on one side, and +5.00 on the other. That makes the net contribution -1.00 μC/m to the left of point B. So the field lines due to the left hand sheet should be to the left for point B.

 

[MitsuShai]

Perhaps in the answer sheet they were summing the contributions to the field from both sides of each plastic sheet.

In the case of the left hand sheet, it has a charge density of -6.00 μC/m^2 on one side, and +5.00 on the other. That makes the net contribution -1.00 μC/m to the left of point B. So the field lines due to the left hand sheet should be to the left for point B.

I attached the answer sheet and it doesn't seem like it; they change the charge density of 1 to positive sometimes...I just don't understand it.

 

[gneill]

Looking at the answer sheet it seems as thought they are taking a positive field to be pointing to the left. That is, when at a given location field lines from a source point to the left it is considered positive, and when they point to the right, it is negative.

I don't know why they would have chosen such a convention. It is possible that at some time the values of the charge densities were changed in order to 'change' the question, and the the answer key was not updated to reflect the situation.

 

[MitsuShai]

Looking at the answer sheet it seems as thought they are taking a positive field to be pointing to the left. That is, when at a given location field lines from a source point to the left it is considered positive, and when they point to the right, it is negative.

I don't know why they would have chosen such a convention. It is possible that at some time the values of the charge densities were changed in order to 'change' the question, and the the answer key was not updated to reflect the situation.

I don't understand how to solve this problem as in I don't know how to determine the signs according to the points A,B, and C.

 

[gneill]

I don't understand how to solve this problem as in I don't know how to determine the signs according to the points A,B, and C.

See what happens if you assume that field lines pointing to the left indicate a positive field direction.

 

[MitsuShai]

See what happens if you assume that field lines pointing to the left indicate a positive field direction.

The direction of the charge density suppose to be different for each point, A,B and C but I can't figure out how.

Like for point A, only the charge density of 1 is in the negative direction, but the others aren't...I mean even if the left indicates a positive field direction there are three other charge densities going in the same direction as the first one.
I'm thinking that the position of the points somehow influence the charge densities.

 

[gneill]

It's not the charge densities that are influenced by position, but the perceived direction of the fields they produce. For example, a positive point charge produces a radial field that points outwards in every direction. Stand to the left of it and the field points to the left. Stand to the right and the field points to the right. Stand above the charge and the field is pointing upwards. For a negative charge the field direction always points towards the negative charge.

A similar situation holds for a sheet of charge. The field lines for a positive sheet point outwards from both sides of the sheet. For a negative sheet they point inwards (towards the sheet).

At a given point, the contribution from every sheet can be labeled "left" or "right". Sum up the left contributions. Sum up the right contributions. The larger value determines the net direction, and the net value is the difference between the sums.