Electric Potential and Capacitance

[psmurty2000]

I know that Electrostatic Potential at a point due to a point charge is defined as the amount of work done in bringing a unit positive charge to that point (working against the electric force)

But, I am unable to reconcile this definition with the phrases like "Potential of a conductor"

More specifically, I read that "The potential of a conductor increases as we deposit more charges on it"

First of all, what is meant by potential of a conductor? Potential due to what?

Secondly, why should the potential increase linearly with the charge?

If someone could answer, I would appreciate it
Thankyou
P.S.Murty

 

[ZapperZ]

I know that Electrostatic Potential at a point due to a point charge is defined as the amount of work done in bringing a unit positive charge to that point (working against the electric force)

But, I am unable to reconcile this definition with the phrases like "Potential of a conductor"

More specifically, I read that "The potential of a conductor increases as we deposit more charges on it"

First of all, what is meant by potential of a conductor? Potential due to what?

Secondly, why should the potential increase linearly with the charge?

If someone could answer, I would appreciate it
Thankyou
P.S.Murty

What you described earlier is not the electrostatic potential, but rather the electronstatic potential energy. That's why you can equate it to work done. This has units of energy.

The electrostatic potential has units of "volts" or equivalent. This also has a dimension of energy/unit charge. However, because "potential" and "potential energy" are really measured either as a CHANGE or with respect to a reference value, one can sometime use the term "potential difference".

Now I'm saying that because you included a "capacitance" in the title even though you said nothing about a capacitor in your post. So I will assume that what you mean by adding charge to a conductor means you add charge to one plate of a capacitor. What this can do is to increase the potential difference between the two sides of a capacitor. The "V" or potential difference in volts is now different. Or you can say the amount of work done per unit charge in moving a charge from one plate to the other is equivalent to V. You can also say the amount of work done in moving a charge q from one plate to the other is qV, etc... etc.

You may also want to read this thread:

https://www.physicsforums.com/showthread.php?t=117946

Zz.

 

[astrokreng]

The potential of a conductor refers to the electrostatic potential energy per unit charge at a particular point on the surface of the conductor. It is a measure of the energy required to bring a unit positive charge from infinity to that point on the conductor's surface. This potential is due to the presence of electric charges on the conductor, and it is influenced by the distribution of these charges.

When we deposit more charges on a conductor, the distribution of charges on the conductor's surface changes, and this affects the electric potential. According to the definition of electric potential, the more charges there are on the conductor, the more work is required to bring a unit positive charge to a particular point on the surface. This results in an increase in the potential of the conductor.

The potential of a conductor does not necessarily increase linearly with the charge. It depends on the distribution of charges on the conductor's surface. If the charges are evenly distributed, the potential will increase linearly with the charge. However, if the charges are unevenly distributed, the potential may not increase linearly. This is because the potential is influenced by the distance between charges and their arrangement on the conductor's surface.

I hope this helps to clarify the concept of potential of a conductor and its relationship with the charges on the surface. It is important to note that the concept of potential is a fundamental aspect of electrostatics and is crucial in understanding the behavior of conductors and other electrical systems.