The potential electric and vector potential of a moving charge

In summary, the conversation discusses applying the Liénard-WIechert equations and finding the condition that needs to be satisfied for the particle to be at a certain position. It also mentions the potential electric and the Lorenz gauge. The speaker is asking for confirmation on their understanding of the topic.
  • #1
LCSphysicist
644
161
Homework Statement
.
Relevant Equations
.
Captura de tela de 2022-06-10 17-45-02.png

I could try to apply the Liénard-WIechert equations immediatally, but i am not sure if i understand it appropriately, so i tried to find by myself, and would like to know if you agree with me.

When the information arrives in ##P##, the particle will be at ##r##, such that this condition need to be satisfied:
$$\frac{(vt-r)^2}{v^2} = \frac{r^2+b^2}{c^2} (1)$$

So, we have $$\phi = \frac{kq}{s} = \frac{kq}{r}$$
Also, $$ \vec A = \frac{\mu}{4\pi} \int \frac{J' dV'}{|r-r'|} = \frac{\mu}{4\pi} \frac{q v}{|r|}$$

such that r satisfies ##(1)##.

Is it right? Do you agree with it? I am asking because i remember to read somewhere that the potential electric not necessarilly need to move at speed of light, but i think this is the case in Lorenz gauge. I haven't assumed any gauge here.
 
Physics news on Phys.org
  • #2
  • Like
Likes BvU

1. What is the difference between electric potential and vector potential?

The electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. It is a measure of the work required to move a unit charge from infinity to that point. On the other hand, the vector potential is a vector quantity that represents the magnetic potential field created by a moving charge. It is related to the electric current and is used to calculate the magnetic field.

2. How is the potential electric and vector potential of a moving charge related?

The potential electric and vector potential of a moving charge are related through Maxwell's equations. The electric potential is related to the charge density, while the vector potential is related to the current density. These equations describe the fundamental relationship between electric and magnetic fields and their sources.

3. Can the potential electric and vector potential of a moving charge be measured?

Yes, the potential electric and vector potential of a moving charge can be measured using various experimental techniques. For example, the electric potential can be measured using a voltmeter, while the vector potential can be measured using a magnetometer. These measurements can provide valuable information about the behavior of electric and magnetic fields.

4. How does the potential electric and vector potential of a moving charge affect its surroundings?

The potential electric and vector potential of a moving charge can affect its surroundings in several ways. The electric potential can influence the movement of other charges in the vicinity, while the vector potential can create a magnetic field that can interact with other magnetic fields. These effects can have significant implications in various physical phenomena, such as electromagnetic induction and the behavior of charged particles in a magnetic field.

5. How is the potential electric and vector potential of a moving charge used in practical applications?

The potential electric and vector potential of a moving charge have numerous practical applications. For example, they are used in the design of electric motors and generators, electromagnetic devices such as speakers and microphones, and in medical imaging techniques such as magnetic resonance imaging (MRI). They are also essential in understanding the behavior of electromagnetic waves and their transmission in various mediums.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
780
  • Introductory Physics Homework Help
2
Replies
64
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
257
  • Introductory Physics Homework Help
Replies
2
Views
251
  • Introductory Physics Homework Help
Replies
11
Views
597
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
614
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
384
Back
Top