Electric Potential reference value (or zero).

• fog37
In summary, the conversation discussed the electric potential for a point charge and how it can be modified to have a value of 0 at a specific spatial point instead of infinity. It was determined that adding a constant to the potential changes its functional behavior and that this concept is similar to the gravitational potential. The conversation also included an optional exercise to show the relationship between potential energy and height above the Earth's surface.
fog37
Hello forum members,

The electric potential for a point charge is a scalar function given by $$V = \frac {kq}{r}$$

This means that the potential has a nonzero value everywhere. The potential becomes ##V=0## when ##r=\infty##. However we know that what matters is the potential difference ##\Delta V## and not the absolute value of potential at each spatial point. This is because the physically important and measurable quantities like force and electric field depend on that difference and not on the absolute value of V at each spatial point...

How would we make the potential to be ##V=0## not at infinity but at different spatial point, like ##r= 5##? How do we modify the function ##V = \frac {kq}{r}##? Like this
$$V = \frac {kq}{r-5}$$

Is that it?

Thanks,
fog37

No, that changes the functional behaviour of the potential, it would diverge at r = 5 instead of r = 0. What is physically irrelevant is a constant addition to the potential.

Oh, you are right.

For instance, something like this: $$V = \frac {kq}{r} + 5$$

So at ##r=\infty## the potential is 5 and wherever the term ##V = \frac {kq}{r}## equals ##-5## the potential will become ##V=0##

Thanks

The gravitational potential is similar. With the reference point at infinity, the gravitational potential outside the Earth's surface is ##V = -GM/r## where ##M## is the mass of the Earth and ##r## is the distance from the center of the Earth. You can reset the reference point to make the potential zero at the Earth's surface by adding a constant: $$V = -\frac {GM} r + \frac {GM} R = GM \left( \frac 1 R - \frac 1 r \right)$$ where ##R## is the radius of the Earth.

Optional exercise: let ##r = R + h## where ##h## is the height above the Earth's sufrace, and show that if ##h \ll R##, then ##V \approx gh## (note little ##g## not big ##G##), so the potential energy of a mass ##m## at height ##h## is ##\approx mgh##.

Ibix

1. What is the concept of electric potential reference value?

The electric potential reference value, also known as electric potential zero, is a point of reference used to measure the potential difference between two points in an electric field. It is usually chosen as the point where the electric potential is considered to be zero.

2. How is the electric potential reference value determined?

The electric potential reference value is typically determined by the location of a point where the electric potential is known to be zero. This could be the surface of a conductor or a point infinitely far away from any charged object.

3. Why is the concept of electric potential reference value important?

The electric potential reference value is important because it allows us to measure and compare the potential difference between different points in an electric field. It is also crucial in calculating the electric potential at a specific point, which is essential in understanding the behavior of electric charges.

4. Can the electric potential reference value change?

Yes, the electric potential reference value can change depending on the context. For example, if the reference point is chosen as the surface of a charged object, the electric potential reference value will change if the charge on that object changes.

5. How does the concept of electric potential reference value relate to electric potential energy?

The electric potential reference value and electric potential energy are closely related. The electric potential energy of a charged object is directly proportional to its electric potential with respect to the reference value. This means that a change in the reference value will result in a corresponding change in the electric potential energy of the object.

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