# Three charges located on a straight line

• yzphysics
In summary: The direction of the force exerted by Q1 on Q3 is down the line.The direction of the force exerted by Q2 on Q3 is down the line.
yzphysics

## Homework Statement

Three charges, Q1, Q2 and Q3 are located on a straight line. The charge Q3 is located 0.169 m to the right of Q2. The charges Q1 = 1.56 μC and Q2 = -3.03 μC are fixed at their positions, distance 0.268 m apart, and the charge Q3 = 3.18 μC could be moved along the line. For what position of Q3 relative to Q1 is the net force on Q3 due to Q1 and Q2 zero? Give your answer in meters, and use the plus sign for Q3 to the right of Q1.

## Homework Equations

Coulomb's Law: F=(k(q^2))/r^2

## The Attempt at a Solution

(k*Q3*Q2)/r^2 = (k*Q3*Q1)/ (r+0.268)^2

After setting it up, I noticed that k and Q3 on both sides cancel out which leaves me with:
(Q2)/r^2 = (Q1)/ (r+0.268)^2

(3.02*10^-6)/r^2 = (1.56*10^-6)/(r+0.268)^2

Then, I got a quadratic formula: 1.47*r^2 + 1.62*r +.2176

so r is equal to -0.157m and -0.945m

but none of the two is right. What am I doing wrong?

Your equation assumes that Q3 is to the right of Q2. That's why your solutions do not make sense. What other region can you try?

Generally, it's a good idea to figure out which region makes sense before you try to solve for the exact location.

I thought that "charge Q3 is located 0.169 m to the right of Q2" means that the point charges are at this order Q1---------Q2----.169-------Q3

Are the point charges supposed to be at this order: Q1------Q3-----Q2?

yzphysics said:
I thought that "charge Q3 is located 0.169 m to the right of Q2" means that the point charges are at this order Q1---------Q2----.169-------Q3
Sure, that's what that means, of course. But then they said you can slide Q3 around. (So I have no idea why they gave you an initial position for Q3, unless there are multiple parts to this problem.)

Would you set up Q3 to be between Q1 and Q2?

yzphysics said:
Would you set up Q3 to be between Q1 and Q2?
Consider the directions of the forces on Q3. Could they cancel in that region?

When Q3 is placed between Q1 and Q2, it will cause the charge to move like this: <--Q1 (+), Q3 (+)-->, Q2 (-)
So overall, the charge does cancels out.

yzphysics said:
When Q3 is placed between Q1 and Q2, it will cause the charge to move like this: <--Q1 (+), Q3 (+)-->, Q2 (-)
So overall, the charge does cancels out.
Rethink this. What is the direction of the force exerted by Q1 on Q3? The force exerted by Q2 on Q3?

## 1. What is the electric potential at a point on the line between the three charges?

The electric potential at a point on the line between the three charges can be calculated by adding the individual electric potentials of each charge at that point. The electric potential due to a point charge is given by the equation V = kQ/r, where k is the Coulomb's constant, Q is the charge, and r is the distance from the charge to the point in question. Therefore, to find the electric potential at a point on the line, we need to determine the distances from each charge to that point and add their individual potentials together.

## 2. How do the charges affect each other's electric fields?

The charges on the line will create individual electric fields that will interact with each other. The direction and strength of the electric fields will depend on the charges' magnitudes and distances from each other. If two charges have the same sign, their electric fields will repel each other, while opposite charges will attract. The overall electric field at any point on the line is the vector sum of the individual fields created by each charge.

## 3. What is the net force on a charge placed on the line between the other two charges?

The net force on a charge placed on the line between the other two charges can be calculated using Coulomb's law. The force on a charge due to another charge is given by the equation F = kQq/r^2, where k is the Coulomb's constant, Q and q are the charges, and r is the distance between them. To find the net force, we need to calculate the individual forces from each charge and add them together. The direction of the net force will depend on the charges' signs, with like charges repelling each other and opposite charges attracting.

## 4. How does the location of the charges on the line affect the electric potential at a point?

The location of the charges on the line will affect the electric potential at a point because the distance between the charges and the point in question will change. The electric potential decreases as the distance from the charge increases. Therefore, the closer the charges are to the point, the higher the electric potential will be, and vice versa. Additionally, the relative magnitudes and signs of the charges will also affect the electric potential at a point.

## 5. Can the electric potential at a point on the line ever be zero?

Yes, the electric potential at a point on the line can be zero if the net electric potential due to all three charges is zero. This can happen when the charges have equal and opposite magnitudes and are symmetrically placed on either side of the point. In this case, the individual electric potentials from each charge will cancel out, resulting in a net electric potential of zero at the point.

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