# Electric field unknown charge problem

## Homework Statement

Two known charges, -12MC and 45 MC, and a third unknown charge are located on the x-axis. The charge -12 MC is at the origin, and the charge 45.0 MC is at x= 0.15 cm. The unknown charge is to be placed so that each charge is in equilibrium under the action of the electric forces exerted by the other two charges. Is this possible? Find the required location, magnitude and sign of the unknown charge.

## The Attempt at a Solution

What I did first was to assume that the unknown charge is to the right of the -12 MC charge and when I set the forces of each of the known charges with the unknown charge equal to each other, I got a distance of 0.0160 m to the left of the -12 MC (though I'm not sure if it's right)...but then I think that the charge could be both positive and negative at the same location which I think makes sense. The trouble is how to find the magnitude after that...I tried finding the Electric field on the unknown charge by the two other known charges but that didn't really work...this is really frustrating!!

ehild
Homework Helper
Yes, you are right, the unknown charge can be both positive and negative - if the other two charges are fixed. Yes, the only possible position is on the left from the origin, but it is 0.0016 m - take care of the zeros.
You know the position of the added charge, now you have to decide its possible sign and magnitude so as the other two charges be in equilibrium. Look at the charge at the origin. Find the direction of forces both from the unknown charge and the other 45 MC charge. When are they opposite?

ehild

Yes, you are right, the unknown charge can be both positive and negative - if the other two charges are fixed. Yes, the only possible position is on the left from the origin, but it is 0.0016 m - take care of the zeros.
You know the position of the added charge, now you have to decide its possible sign and magnitude so as the other two charges be in equilibrium. Look at the charge at the origin. Find the direction of forces both from the unknown charge and the other 45 MC charge. When are they opposite?

ehild

So when I tried out the question following your guidelines...I found that the unknown charge can be only positive since the electric forces acting on the charge at the origin by the other two charges end up canceling each other. From there, I set the two equations of the electric forces acting at the origin and found that the unknown charge is 5.12 X10^-9 C. But then when I considered the unknown charge to be negative, both forces acting on the charge at the origin lie both towards the positive x axis (so they don't end up canceling each other out)...so the unknown charge can only be positive and NOT negative...

But then there's another problem, when I calculate the unknown charge from the 45 MC charge at 15 cm to the right of the origin, I get 1.22 X 10^5 C..which is different...
does this mean that this situation is not possible?

Last edited:
ehild
Homework Helper
But then there's another problem, when I calculate the unknown charge from the 45 MC charge at 15 cm to the right of the origin, I get 1.22 X 10^5 C..which is different...
does this mean that this situation is not possible?

Check your calculation, it should work! Nothing is at 15 cm from the origin, it is 0.15... the sign is good, the charge is 51,3 MC - by the way, what does this M mean? and you get the same value from both condition.

ehild