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Chapter 12: Q58P (page 570)

Show that the Liénard-Wiechert potentials (Eqs. 10.46 and 10.47) can be expressed in relativistic notation as

Short Answer

Expert verified

The Liénard-Wiechert potentials in the relativistic notation expressed as

Step by step solution

01

Expression for the ordinary velocity:

Using equations 12.40 and 12.40, write the equation for the spatial part of a 4-vector.

Here, ημ is the proper velocity, y is the Lorentz contraction, c is the speed of light, and v is the ordinary velocity.

02

Determine the Liénard-Wiechert potentials in relativistic notations:

It is given that:

Write the above equation in the implicit form.

Hence, the product of ημand rv becomes,

Using equation 10.46, write the equation for the retarded potentials.

Substitute in the above expression.


Solve the R.H.S of the above equation.

Now, write the above equation in the relativistic notations as:

Therefore, the Liénard-Wiechert potentials in the relativistic notation expressed

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Most popular questions from this chapter

Prove that the symmetry (or antisymmetry) of a tensor is preserved by Lorentz transformation (that is: if is symmetric, show that is also symmetric, and likewise for antisymmetric).

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Whereθis the angle between u and F.
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