/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q58P Show that the Li茅nard-Wiechert ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q58P (page 570)

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

Short Answer

Expert verified

The Li茅nard-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, 畏渭 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 畏渭and 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 Li茅nard-Wiechert potentials in the relativistic notation expressed

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A straight wire along thez-axis carries a charge density位traveling in the +z direction at speed v. Construct the field tensor and the dual tensor at the point role="math" localid="1654331549769" (x,0,0).

12.48: An electromagnetic plane wave of (angular) frequency 蝇is travelling in the xdirection through the vacuum. It is polarized in the ydirection, and the amplitude of the electric field is Eo.

(a) Write down the electric and magnetic fields, role="math" localid="1658134257504" E(x,y,z,t)and B(x,y,z,t)[Be sure to define any auxiliary quantities you introduce, in terms of 蝇, Eo, and the constants of nature.]

(b) This same wave is observed from an inertial system S鈫�moving in thexdirection with speed vrelative to the original system S. Find the electric and magnetic fields in S鈫�, and express them in terms of the role="math" localid="1658134499928" S鈫�coordinates: E(x鈫�,y鈫�,z鈫�,t鈫�)and B(x鈫�,y鈫�,z鈫�,t鈫�). [Again, be sure to define any auxiliary quantities you introduce.]

(c) What is the frequency 蝇鈫�of the wave in S鈫�? Interpret this result. What is the wavelength 位鈫�of the wave in S鈫�? From 蝇鈫�and 位鈫�, determine the speed of the waves in S鈫�. Is it what you expected?

(d) What is the ratio of the intensity in to the intensity in? As a youth, Einstein wondered what an electromagnetic wave would like if you could run along beside it at the speed of light. What can you tell him about the amplitude, frequency, and intensity of the wave, as approaches ?

Inertial system S moves at constant velocity v=尾肠(肠辞蝉蠒x^+蝉颈苍蠒y^)with respect to S. Their axes are parallel to one other, and their origins coincide at data-custom-editor="chemistry" t=t=0, as usual. Find the Lorentz transformation matrix A.

Use the Larmor formula (Eq. 11.70) and special relativity to derive the Lienard formula (Eq. 11. 73).

P=渭0q2a26蟺c鈥夆赌夆赌�(11.70)P=渭0q2纬66蟺c(a2-|蠀脳ac|2)鈥夆赌夆赌�(11.73)

Find the velocity of the muon in Ex. 12.8.
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Astrophysics

Read Explanation

Famous Physicists

Read Explanation

Wave Optics

Read Explanation

Electromagnetism

Read Explanation

Fluids

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.