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

In summary, the charge in the denominator of equations for voltage and electrostatic potential is not dependent on charge. It was originally included in the derivation of the formula for voltage, but it is not necessary and can be simplified by using a scalar field. This concept is similar to gravitational potential, where the mass is defined as the work needed to accelerate an object to a given speed.
  • #1
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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  • #2
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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  • #3
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.
 

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

Why is the charge in the denominator of the equation for voltage?

The charge in the denominator of the equation for voltage, also known as Coulomb's law, is a fundamental part of understanding the relationship between electric charge and electric potential. It represents the force between two charges, with the magnitude of the force decreasing as the distance between the charges increases. This is why the charge is in the denominator - as the distance increases, the force decreases and the resulting voltage is lower.

What does the charge in the denominator of the equation for voltage represent?

The charge in the denominator of the equation for voltage represents the electric charge of the two objects interacting with each other. This charge can be positive or negative, and the magnitude of the charge determines the strength of the electric force between the objects. The charge in the denominator is essential in calculating the resulting voltage between the two objects.

How does the charge in the denominator affect the resulting voltage?

The charge in the denominator of the voltage equation has an inverse relationship with the resulting voltage. This means that as the charge increases, the resulting voltage decreases, and vice versa. This is because the stronger the electric force between two charges, the lower the resulting voltage will be.

Can the charge in the denominator be zero?

No, the charge in the denominator cannot be zero. If the charge were to be zero, it would result in a division by zero, which is undefined. This would make the voltage equation invalid and unable to accurately calculate the resulting voltage between two objects.

How does the charge in the denominator relate to electric potential energy?

The charge in the denominator of the voltage equation is directly related to electric potential energy. As the distance between two charges increases, the electric potential energy decreases. This is because the electric force between the charges also decreases, resulting in a lower voltage. Therefore, the charge in the denominator plays a crucial role in determining the amount of electric potential energy between two objects.

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