Finding Equilibrium Position for Third Charge in Line of Point Charges

In summary, the problem involves two point charges on the x-axis, with a charge of +8.4 µC at the origin and a charge of -3.8 µC at x = 10.0 cm. The question is asking for the position x where a third charge q3 would be in equilibrium. The relevant equation is F=(kq1q2)/r^2, where q1 and q2 represent the two known charges, and q3 is the unknown charge. However, since there is no information given about the relationship between the charges, q3 cannot be eliminated and a solution cannot be found.
  • #1
map7s
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Homework Statement


Two point charges lie on the x axis. A charge of +8.4 µC is at the origin, and a charge of -3.8 µC is at x = 10.0 cm.
At what position x would a third charge q3 be in equilibrium?


Homework Equations


F=(kq1 q2)/r^2


The Attempt at a Solution


I think that my main problem was that I wasn't quite sure how to solve for the distance if I don't have the charge for the third particle or its relation to the other charges.
 
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  • #2
Then, simply use q3 as the value each time you plug it into your relevant equation. It should cancel out later.
 
  • #3
I tried that, but the q3 doesn't cancel out and I don't know how to get rid of it because they don't state any relationships between the charges. (ex: q1=q, q2=-3q, etc.)
 

FAQ: Finding Equilibrium Position for Third Charge in Line of Point Charges

What is a point charge on a line?

A point charge on a line is a simple model used in physics to represent the electric field produced by an infinitely long line of charge. It is a hypothetical situation where all the charge is concentrated at a single point on the line.

How is the electric field calculated for point charges on a line?

The electric field for point charges on a line is calculated using the equation E = kλ/r, where k is the Coulomb's constant, λ is the linear charge density (charge per unit length) of the line, and r is the distance from the point charge to the line.

Can point charges on a line have different magnitudes and signs?

Yes, point charges on a line can have different magnitudes and signs. In fact, this is often the case in real-world situations. The electric field produced by a positive point charge on a line is in the opposite direction of that produced by a negative point charge on the same line.

How does the electric field change as the distance from the point charge increases?

The electric field produced by point charges on a line decreases as the distance from the point charge increases. This is because the electric field strength is inversely proportional to the square of the distance from the point charge.

Is a point charge on a line an idealized situation?

Yes, a point charge on a line is an idealized situation used in theoretical calculations. In reality, charges are distributed over a finite length, and the electric field is not perfectly uniform. However, the point charge on a line model is still useful in understanding the behavior of electric fields in certain situations.

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