How do I solve where the absolute potential should be zero?

[Vladi]

Homework Statement

A point charge of + 2.0 μC is placed at the origin of coordinates. A second, of − 3.0 μC, is placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute potential be zero?

Homework Equations

V= ko*∑ (q/r)

The Attempt at a Solution

My work is attached to this post. In the attachment, you will find my calculations which were based off of my drawing and the relevant equation provided. I also included the answer to the problem within the attachment.

 

[mjc123]

I agree with your answer of X0 = 2 m (i.e. x = -2 m). I think the given answer of x = -0.2 m is a mistake. Can you see where x = 40 cm comes from?

 

[Vladi]

Thank you for the quick reply. Schaum's Outline of College Physics does have some typos. I guess this could be one of them. Suppose the absolute potential is somewhere between the two charges in the given prompt. This would imply that the distance between the equilibrium point and the origin is x1. This would also imply that the distance between the charge on the 100 cm mark and the equilibrium point would be 1m-x1. After I plugged these numbers in the relevant equation, I get x=40cm. I get this anwser, but it makes no sense to me. I thought equilibrium points only occur where the magnitudes of the charges are capable of cancelling each other out. How is this answer possible?

 

[haruspex]

equilibrium points only occur where the magnitudes of the charges are capable of cancelling each other out.

Neither is an equilibrium point. An equilibrium point is where the fields cancel. The question asks you to find where the net potential is zero.

 

[Vladi]

Neither is an equilibrium point. An equilibrium point is where the fields cancel. The question asks you to find where the net potential is zero.

It sounds like I'm confusing the two. How do I go about determining where the net potential is zero?

 

[haruspex]

It sounds like I'm confusing the two. How do I go about determining where the net potential is zero?

Your method was basically sound, but did not find all solutions.
The complication with potential is that the formula is $\frac{kq}{|r|}$. That modulus sign introduces extra possible solutions.
For equilibrium, i.e. zero field, it is 1/r², but now the complication is that it is a vector.

 

[Vladi]

Your method was basically sound, but did not find all solutions.
The complication with potential is that the formula is $\frac{kq}{|r|}$. That modulus sign introduces extra possible solutions.
For equilibrium, i.e. zero field, it is 1/r², but now the complication is that it is a vector.

If I understood you correctly, the relevant equation that I provided is useless if I do not include the absolute value bars. I re-did my calculations from the first part and got that x0=-.4m and x0=2m. This must imply that the absolute potential is zero at a point 2 meters to the left of charge a. The absolute potential is also zero at a point 40cm to the right of charge a. My calculations have been attached to this reply. Is this correct? Thank you for your time. It is much appreciated.

 

[haruspex]

the relevant equation that I provided is useless if I do not include the absolute value bars.

Not useless, just not general enough.

The absolute potential is also zero at a point 40cm to the right of charge a.

Yes.

 

[Vladi]

Not useless, just not general enough.

Yes.

Thank you for all your help. I think I'll understand how to tackle such problems in the future.