# E&M fields of a moving point charge

• meteorologist1
In summary, the fields on the x-axis to the RIGHT of the point charge q are described by the formula \vec{E} = \frac{q}{4\pi\epsilon_0}\frac{1}{r^2}(\frac{c+v}{c-v})\hat{x} and \vec{B} = 0, while the fields on the x-axis to the LEFT of the charge are given by \vec{E} = \frac{q}{4\pi\epsilon_0}\frac{1}{r^2}(\frac{c-v}{c+v})\hat{x} and \vec{B} = 0. This can be derived using the Lienard-Wie
meteorologist1
Hi, I need help on the following question: Suppose a point charge q is constrained to move along the x-axis. Show that the fields at points on the axis to the RIGHT of the charge are given by

$$\vec{E} = \frac{q}{4\pi\epsilon_0}\frac{1}{r^2}(\frac{c+v}{c-v})\hat{x}$$ and $$\vec{B} = 0$$

What are the fields on the axis to the LEFT of the charge?

I'm thinking that I need to use the two formulas for E and B which are derived from the Lienard-Wiechert potentials.
See here: http://scienceworld.wolfram.com/physics/PointCharge.html

Thanks.

The fields at points on the axis to the LEFT of the charge are given by \vec{E} = \frac{q}{4\pi\epsilon_0}\frac{1}{r^2}(\frac{c-v}{c+v})\hat{x} and \vec{B} = 0

Hello! Thank you for reaching out for help with this question. The equations you have provided for the electric and magnetic fields of a moving point charge are correct. They are derived from the Lienard-Wiechert potentials, which describe the electromagnetic fields of a moving point charge in terms of its position, velocity, and acceleration.

To show that these equations are valid, we can use the method of images. This method involves creating a "mirror charge" that is equal in magnitude but opposite in sign to the original charge, placed at a distance r from the original charge on the opposite side of the x-axis. This creates an electric field that is equal and opposite to the original charge's field, canceling it out on the x-axis.

Using this method, we can see that the electric field on the axis to the LEFT of the charge is also given by the equation you provided, but with a negative sign. This makes sense, as the electric field should be pointing in the opposite direction on the left side of the charge compared to the right side.

As for the magnetic field, it is zero on both sides of the charge. This is because a moving point charge only produces a magnetic field when it is accelerating, and since it is constrained to move along the x-axis, there is no acceleration.

I hope this explanation helps you understand the fields of a moving point charge along the x-axis. If you have any further questions, please don't hesitate to ask. Good luck with your studies!

## 1. What is an E&M field?

An E&M (electromagnetic) field is a physical field that is created by the presence of electrically charged particles. It consists of electric and magnetic components, and is a fundamental concept in physics that explains the behavior of charged particles and their interaction with each other and with other objects.

## 2. How does a moving point charge create an E&M field?

A moving point charge creates an E&M field because it has an electric charge, which is a fundamental property of matter. As the charge moves, it creates an electric field that radiates outward in all directions. The motion of the charge also creates a magnetic field, which is perpendicular to the electric field and also radiates outward.

## 3. How does the strength of the E&M field change when a point charge moves?

The strength of the E&M field created by a moving point charge depends on the speed of the charge and its distance from other objects. As the charge moves faster, the strength of the field increases. Similarly, the closer the charge is to another object, the stronger the field will be at that location.

## 4. What is the relationship between E&M fields and electromagnetic radiation?

Electromagnetic radiation, such as light and radio waves, is a form of energy that is carried by E&M fields. These fields oscillate in a specific pattern and produce waves that travel through space at the speed of light. As a result, E&M fields and electromagnetic radiation are closely related and are both essential for understanding many physical phenomena.

## 5. How are E&M fields of a moving point charge related to the concept of relativity?

The concept of relativity states that the laws of physics are the same for all observers, regardless of their relative motion. E&M fields of a moving point charge are affected by this principle, as the strength and direction of the fields can appear different to different observers depending on their relative motion. This is known as the Lorentz transformation, and it is a crucial aspect of understanding the behavior of E&M fields in relation to moving objects.

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