Deriving electromagnetic fieldfor point charge

In summary, The derivation for the electromagnetic field of point charges by Griffith can be found on page 437 of his book "Introduction to Electrodynamics." The formula for the triple cross products is used to obtain the final result, but a minus sign should be included in the rule for the triple cross products. This was a simple mistake that was corrected.
  • #1
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Hi all,

I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437).

I'm missing minus sign somewhere:

The book says that:[itex]\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla tr)+\vec{v}-\vec{v}(\vec{v}\cdot\nabla tr)-\vec{n}\times(\vec{a}\times \nabla tr)+\vec{v}\times (\vec{v}\times \nabla tr)[/itex]

Using the rule for triple cross products gives:

[itex]\vec{v}+(v^{2}-\vec{n}\cdot\vec{a})\nabla tr[/itex]

However is should be:

[itex]\vec{v}+(-v^{2}+\vec{n}\cdot\vec{a})\nabla tr[/itex]


I'm sure I am missing something.

Thanks
 
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  • #2
oh I've got it. Forgot the minus sign in the triple cross product rule :$
 

1. What is the equation for deriving the electromagnetic field for a point charge?

The equation for deriving the electromagnetic field for a point charge is given by the Maxwell's equations, specifically the Gauss's law for electric fields and the Ampere's law, in combination with the Lorentz force law.

2. How is the electromagnetic field for a point charge calculated?

The electromagnetic field for a point charge can be calculated by using the Coulomb's law, which describes the electric force between two charges, and the Biot-Savart law, which describes the magnetic field produced by a moving charge. These two laws can be combined to calculate the total electromagnetic field for a point charge.

3. What factors affect the strength of the electromagnetic field for a point charge?

The strength of the electromagnetic field for a point charge is affected by the magnitude of the charge, the distance from the charge, and the speed of the charge's movement. Additionally, the presence of other charges or magnetic materials in the surrounding environment can also affect the strength of the field.

4. How does the electromagnetic field for a point charge behave in different environments?

The behavior of the electromagnetic field for a point charge can vary depending on the environment it is in. In a vacuum, the field will follow the inverse square law, meaning its strength decreases with the square of the distance from the charge. In a medium with different electrical properties, the field may behave differently due to polarization and other factors.

5. Can the electromagnetic field for a point charge be measured?

Yes, the electromagnetic field for a point charge can be measured using instruments such as an electromagnetic field meter or a Gauss meter. These instruments can detect and measure the strength and direction of the electromagnetic field at a given point in space.

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