# Elementry Electrostatics question

• 838
In summary: To find the point where the forces cancel, you want to choose the root that corresponds to the point where the forces point in opposite directions. This is the point with a negative value, as it is located to the left of the charge at x=0. Therefore, the correct answer is a = -24.14 cm.In summary, the net electrostatic force on a third charge of +20 nC placed between two point charges (q1=+20 nC and q2=-40 nC) placed 10.0 cm apart on the x-axis can be cancelled by placing the third charge at a distance of -24.14 cm from the origin. This is found by setting the forces between the charges to equal and solving
838

## Homework Statement

Two point charges (q1=+20 nC and q2=-40 nC) are placed 10.0 cm apart onlong the x-axis. Where can a third charge (q3=+20 nC) be placed so that the net electrostatic force on that charge is zero?

F=k(q1q2)/r^2

## The Attempt at a Solution

It's definitely not a hard problem, I'm guessing I'm supposed to set the entire equation into equilibrium. Other than that basic concept, I really don't understand how to solve for this problem. My professor only went over calculating forces between two charges.

Thanks for any help, I could really use it. :(

Place q1 at x=0 and q2 at x=10, and put q3 at x=a. Now write the two forces on q3 as a function of a, set them equal and solve for a. It's helpful when you do this to figure out what portion of the line you expect q3 to be on first. Will a<0, 0<a<10 or a>10?

So if I'm understanding you correctly, it should look like this:

k*(q1q3)/a^2=k*(q2q3)/(10+a)^2 since a < 0. I think...

So we get a = 4.14

To test this, I can calculate the force between q1 and q3 and match it with q2 and q3, since they should be equal.

So, k*(q1q3)/(4.14^2) = 23.31k
and k*(q2q3)/(10-4.14)^2=23.31k.

Should be correct. Any errors?

Thanks.

Careful! I think you are picking the wrong root. You want solve k*(q1q3)/a^2=k*(q2q3)/(10-a)^2 if a<0 is the coordinate of the point. If you solve that you get 4.14 and -24.14. Since you assumed a<0 the one to pick is -24.14. If you call a the distance of the point from the origin then you solve k*(q1q3)/a^2=k*(q2q3)/(10+a)^2 and assuming a>0. You get -4.14, 24.14 and pick the positive one.

Ah, ok, I understand. I wasn't sure which root to choose for. Thanks a lot!

838 said:
Ah, ok, I understand. I wasn't sure which root to choose for. Thanks a lot!

The root you chose corresponds to the point between the charge at x=0 and the charge at x=10. Here the magnitude of the forces are equal, but they point in the same direction.

## What is electrostatics?

Electrostatics is the study of electric charges at rest and the forces and fields associated with these charges.

## What is an electric charge?

An electric charge is a fundamental property of matter that causes it to experience a force in an electric field.

## What is an electric field?

An electric field is a region in space where an electric charge experiences a force.

## What is Coulomb's Law?

Coulomb's Law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## What is an electric dipole?

An electric dipole is a pair of equal and opposite charges separated by a distance, resulting in a net electric dipole moment.

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