Electric Field Lines on a Dipole

Question

The next two questions refer to the following situation: Two charges of equal magnitude but opposite polarity (one +q and one –q) are arranged as shown.

What is the most accurate depiction of the net E-field due to +q and –q at the position labeled Point X? The x- and y-axes shown at Point X are the same as the axes shown in each of the images below.

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Also please note that the number in front of each option is just to help us identify the answer you chose and has no other meaning.

Group of answer choices

5.Where theta is smaller than 45 degrees

4.Where theta is larger than 45 degrees

1. Where theta is larger than 45 degrees

3.Where theta is smaller than 45 degrees

2.Where theta is smaller than 45 degrees

Which electric field lines shown (1 through 5) is correctly drawn? The electric field in question here is the composite field due to both charges, not to any single one. More than one answer may be correct.

Group of answer choices

Line 3

Line 2

Line 5

Line 1

Line 4

Answer 1

Question 1:

The direction of the field at X is the direction of the electrical force that would

act on a small positive charge at X.

That force consists of two components:

Component 1: Force dues the positive charge will be repulsive, pointing along the positive y axis.

Component 2: Force due to the negative charge will be attractive, pointing towards the negative charge.

The distance between the point X and the negative charge is at least double the distance to the positive charge.

Therefore the force due to the positive charge will be at least four time bigger than the force due the negative charge.

Based on these observations we can eliminate some possibilities.

Option 1 is eliminated because it is pointing too far down,

even lower that the direction to the negative charge.

Option 2 is eliminated because it seems to point directly at the negative charge, ignoring the larger effect of the positive charge.

Option 3 is eliminated because the projection of the suggested vector sum is too far down:

Its projection on the y-axis is smaller than the projection on the direction towards the negative charge, although the relationship between the two forces is the opposite.

In the absence of Figure 5, figure 4 looks most correct.

Question 2:

Line 1 can be eliminated because everywhere on the x-axis the field is along the x-axis,

while line 1 shows it pointing down.

Line 2 is eliminated because it is pointing in the opposite direction.

Line 3 is eliminated because it shows a positive test charge as if it were repulsed by the negative charge -q.

Line 4 is eliminated because it shows the field as if unaffected by the negative charge.

Line 5 has the best chance of being correct.