Magnetic field of moving charged particle

In summary, the appropriate way to model the magnetic field of a moving charged point particle is by using the Biot-Savart equation and integrating over a single point. However, for a point particle passing through a conducting loop, there will be no induced azimuthal EMF due to the absence of net magnetic flux linking the loop. The resulting magnetic and electric fields will be azimuthal and radial, respectively, with high amplitude and short duration for relativistic point charges.
  • #1
grundletaint
1
0
What is the appropriate way to model the magnetic field of a moving charged point particle?

I don't believe you can use Biot-Savart because it is not a steady current.

I am trying to figure out what EMF (current) would be induced in a square or round conducting loop when a charged point particle passes through it.

Thanks
 
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  • #2
Maybe BS Equation help, integrating over a single point.

[tex]\vec{B}(\vec{r})=\dfrac{\mu_0}{4\pi}\dfrac{e (\vec{v} \times \hat{r})}{r^2}[/tex]
 
  • #3
The point charged particle moving through a loop will develop an azimuthal magnetic pulse, but because there is no net magnetic flux linking the loop, there will be no induced azimuthal EMF. The magnetic field from either a point charge-current or a steady current is azimuthal, and the electric field is radial. For relativistic point charges, the longitudinal extent of the fields are collapsed by the factor gamma, so the observed pulses are very short, and very high amplitude.
 

1. What is the magnetic field of a moving charged particle?

The magnetic field of a moving charged particle is a region of space around the particle where magnetic forces are present. It is caused by the particle's electric charge and its motion.

2. How is the magnetic field of a moving charged particle calculated?

The magnetic field of a moving charged particle can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current flowing through a conductor and inversely proportional to the distance from the point to the conductor.

3. What is the direction of the magnetic field of a moving charged particle?

The direction of the magnetic field is perpendicular to both the direction of the particle's motion and the direction of the magnetic force acting on the particle. The right-hand rule can be used to determine the direction of the magnetic field.

4. How does the speed of a charged particle affect its magnetic field?

The speed of a charged particle has a direct effect on the strength of its magnetic field. As the particle's speed increases, the strength of the magnetic field also increases. This relationship is described by the equation B = μ0qv/2πr, where B is the magnetic field, μ0 is the permeability of free space, q is the charge of the particle, v is the speed, and r is the distance from the particle.

5. What are some applications of the magnetic field of moving charged particles?

The magnetic field of moving charged particles has many practical applications. It is used in particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. It also plays a crucial role in the functioning of electric motors and generators.

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