Electric Energy: Experiment & Negative Potential

[burak_ilhan]

1)two different formulas for electric field is
a)U=(1/2)Q1V1+(1/2)Q2V2+...

b)$$U=\int \frac{1}{2}\epsilon.E^2dv$$

Using these how could we perform an experiment to test where the energy located?

2)Since the electric energy density is never negative, how can the mutual electric potential of a pair of opposite charges be negative?

My idea on the first one was following an example in the lecture:
radiowave is a very good example that the energy is on the field lines,because even you stop signalling, the field or the wave still exist in space.Any comment is welcome

 

[Nate810]

.To answer the second question, it is important to note that the electric potential of a pair of opposite charges is always relative. This means that the potential of one charge is compared to the potential of the other charge. The mutual electric potential can be negative if the potential of one charge is higher than the potential of the other charge.

 

[M98Ranger]

1) To test where the energy is located, we could perform an experiment using a charged object and a voltmeter. First, we would measure the electric potential at different points around the charged object using the voltmeter. Then, using formula (a), we could calculate the energy at each of those points. This would give us an idea of where the energy is located around the charged object. We could also plot a graph of the potential vs. distance and observe the trend to determine the location of the energy. Additionally, we could use formula (b) to calculate the electric field at different points and compare it to the potential measurements to see how the energy is distributed in the electric field.

2) The mutual electric potential of a pair of opposite charges can be negative because it represents the work done by an external force to bring the two charges together. This work is negative because the external force is acting in the opposite direction of the displacement, resulting in a negative change in potential energy. However, the electric energy density, which is the energy per unit volume, is never negative. This is because the electric field and the energy are always in the same direction and the electric energy density is proportional to the square of the electric field.

 

[M98Ranger]

1) To perform an experiment to test where the energy is located, we could use a charged particle and measure its potential energy at different points in the electric field. We can use the first formula, U=(1/2)Q1V1+(1/2)Q2V2+..., to calculate the potential energy at each point. By doing this at multiple points, we can create a map of the electric field and determine where the energy is located. Another option is to use a device called an electric field sensor, which can measure the strength and direction of the electric field at different points. By moving the sensor around, we can also create a map of the electric field and determine where the energy is located.

2) The mutual electric potential of a pair of opposite charges can be negative because it represents the potential energy of the system. The formula for electric potential, V=kQ/r, takes into account the distance between the charges. When the charges are opposite, the potential energy is negative because the charges are attracted to each other and work is required to separate them. This negative potential energy is then converted into kinetic energy when the charges are allowed to move closer together. Therefore, although the energy density may be positive, the mutual electric potential can still be negative. Your example of a radiowave is a good one, as it also demonstrates that the energy is located in the electric field rather than at the charges themselves.