Invisible Charge: Solving for Equal Distance in Coulomb's Law

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The discussion centers on the concept of "invisible" charge in relation to Coulomb's Law and electric potential. It highlights that when two points, A and B, are equidistant from a charge q1, the electric potentials VA and VB are equal, resulting in a potential difference of zero. This does not imply the absence of charge; rather, it indicates that the charge creates equipotential surfaces where the potential difference remains constant. The analogy to gravitational potential on Earth's surface is used to illustrate that even with uniform potential, the presence of charge or mass is still significant. Ultimately, the charge remains present despite the zero potential difference between the two points.
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"Invisible" charge?

HI all,

Homework Statement


https://www.physicsforums.com/showthread.php?t=427862
See attached picture. q1 is at equal distance from A or B.
k = coulomb's constant

Homework Equations



VA = (k q1 / r)
VB = (k q1 / r)

The Attempt at a Solution



VAB = VA - VB = 0 V

It seems that the charge becomes invisible in that case, right?
 

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The charge is not invisible.

We have (roughly) the same gravitational potential everywhere on the surface of earth. Is Earth invisible? Do you float freely in space?
 
That's right but its effect on voltage difference is the same as if there was no charge.
 
Any charge configuration admits equipotential surfaces. The potential difference between any two points on such a surface is zero. Which does not mean there is no charge.
 

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