# Fundamental problem in electrostatics

• Kolahal Bhattacharya
In summary, the concept of electrostatics involves neglecting magnetic effects and time-varying fields. When a test charge is moving slowly, the resulting electric and magnetic fields will only have small fluctuations. However, if the test charge moves at a significant fraction of the speed of light, these fields will become larger and create a messy calculation. This is why it is said that the test charge should be moving slowly in electrostatics.

#### Kolahal Bhattacharya

Can someone say why it is said that in electrostatics,the test charge may be moving very slowly?Specifically,what is wrong if the test charge moves at a speed which is a significant proper fraction of speed of light?

Kolahal Bhattacharya said:
Can someone say why it is said that in electrostatics,the test charge may be moving very slowly?Specifically,what is wrong if the test charge moves at a speed which is a significant proper fraction of speed of light?

From my little understanding... (warning: which could be wrong )
When you move a charge you create current, which creates a magnetic field, which creates an electric field. The calculation becomes messy. Plus, electrostatics doesn't worry itself with time-varying fields. Also moving a significant fraction of the speed of light then brings in relativistic effects.

I see.Let me concretize:
In electrostatics,we neglect magnetic effects and time varying effects.Now,a single moving charge,even running at a constant speed,results in a non-steady current,and that in turn,will result in a time-varying magnetic field.This,again,will induce a time varying electric field.
Now,if the speed is very small,we will have a slight fluctuation and if the speed is high,the magnitude of current,and hence,the resulting E and B fields will be big.So,electrostatics will make a mess with big fluctuations in fields and magnetic effects.

If people would use CGS or Gaussian units, it would be apparent that the magnetic effects are proportional to v/c, so it's a very small effect indeed. Thus, "slowly" basically means "a negligible fraction of the speed of light".

Yes!Of course.

## What is the fundamental problem in electrostatics?

The fundamental problem in electrostatics is the question of how charges interact with each other and with external electric fields. It is a fundamental aspect of electromagnetism and helps to explain many phenomena, such as how objects can become charged and how electric fields can be created and manipulated.

## What is the difference between electrostatics and electrodynamics?

Electrostatics deals with the behavior of stationary charges and their interaction with electric fields, while electrodynamics includes the study of moving charges and the creation of magnetic fields. In other words, electrostatics is a subset of electrodynamics.

## What is the significance of the Coulomb’s law in electrostatics?

Coulomb's law is a fundamental law in electrostatics that describes the force between two stationary charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is essential in understanding the behavior of electric charges and their interactions.

## What is the role of Gauss’s law in electrostatics?

Gauss's law is a fundamental law in electrostatics that relates the electric field to the distribution of electric charges. It states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space. This law is useful in solving problems involving symmetrical charge distributions.

## How does the fundamental problem in electrostatics relate to real-world applications?

The fundamental problem in electrostatics is the basis for many real-world applications, such as the design of electronic devices, capacitors, and electrostatic precipitators. It is also crucial in understanding natural phenomena, such as lightning, and is used in industries such as energy generation, telecommunications, and medical imaging.