Why do we have a charge in the denominator of equation for voltage?

AI Thread Summary
The discussion centers on the presence of charge in the denominator of voltage equations, questioning its necessity since voltage and electric potential are not directly dependent on charge. It explains that electrostatic potential is defined as electrostatic potential energy per unit charge, making it easier to conceptualize energy in a scalar field. The analogy with gravitational potential illustrates that while energy depends on mass, the potential itself is independent of it. The conversation also touches on the foundational aspects of physics, suggesting that definitions may vary based on what is considered fundamental. Ultimately, the inclusion of charge in voltage equations serves as a useful framework for understanding energy interactions in electric fields.
Callmelucky
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Homework Statement
Why do we have a charge in the denominator of equations for voltage and el. potential if both voltage and el. potential are not dependent on charge?
Relevant Equations
U=W/q, fi=Eep/q (fi=el. potential, Eep= el. pot. energy, U= voltage)
Why do we have a charge in the denominator of equations for voltage and el. potential if both voltage and el. potential are not dependent on charge?
Is it just because that was the only way to derive the formula for voltage and then we realized we don't need q? U=W/q --> U=eqd/q.
 
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It's a definition. Electrostatic potential ##V_e## is electrostatic potential energy ##U_e## per unit charge. The energy does depend on the charge but it is easier to think of a scalar field ##V_e## such that when we place charge ##q## at some point in space, its energy will be ##U_e=qV_e##.

You have already encountered this idea. Compare with something familiar, gravitational potential. Near the surface of the Earth it is ##V_g=gh##. When one puts mass ##m## at height ##h##, its gravitational potential energy is ##U_g=mV_g=mgh.##
 
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To add to @kuruman's reply…
It depends what you take as fundamental. If you take energy, distance and time as fundamental then you would define the mass of an object as the work needed to accelerate it to a given speed.
 
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