Two Charges, Find Spot of Zero Potential

[kgigs6]

Homework Statement

Charges of -q and +2q are fixed in place, with a distance d = 6.00 m between them. A dashed line is drawn through the negative charge, perpendicular to the line between the charges. On the dashed line, at a distance L from the negative charge, there is at least one spot where the total potential is zero. Find the distance L.
http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c19/qu_19.62.gif

Homework Equations

Vtotal = kq1/r1 + kq2/r2

The Attempt at a Solution

Since I'm looking for when vtotal = 0 then -kq/r1 = k2q/r2

I'm lost as to where to go from here, I can't figure out how to use the d=6m. Any help is appreciated!

 

[lanedance]

so find r1 in terms of r2

trhen make use fo the fact that r1, r2 & d make a right triangle

 

[nlightner]

I would approach this problem by first understanding the concept of potential energy and potential difference. The electric potential at a point in space is the amount of work that would be required to bring a unit charge from infinity to that point. In this case, we have two fixed charges, which create an electric field in the space around them. The potential at any point in this electric field can be calculated using the formula V = kq/r, where k is the Coulomb's constant, q is the charge, and r is the distance from the charge.

To find the spot where the total potential is zero, we can use the principle of superposition, which states that the total potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge. In this case, we have two charges, -q and +2q. Using the formula for total potential (Vtotal = kq1/r1 + kq2/r2), we can set it equal to zero and solve for the distance L.

k(-q)/L + k(2q)/(6-L) = 0

Solving for L, we get L = 2.40 m.

This means that at a distance of 2.40 m from the negative charge, on the dashed line, the total potential is zero. This makes sense because at this point, the potential due to the negative charge is equal in magnitude but opposite in sign to the potential due to the positive charge, resulting in a net potential of zero.

In conclusion, by understanding the concept of potential energy and using the principle of superposition, we were able to find the spot of zero potential on the dashed line between the two fixed charges. This approach can be applied to similar problems involving multiple charges and finding points of zero potential.