Question: Using the Lorentz transformations of the (mathbf{E}) and (mathbf{B}) fields, show that (E^{2}-B^{2}) is a Lorentz invariant; that is, show that ({E^{prime}}^{2}-B^{prime 2}=E^{2}-B^{2}).

Using the Lorentz transformations of the $\mathbf{E}$ and $\mathbf{B}$ fields, show that $E^{2}-B^{2}$ is a Lorentz invariant; that is, show that ${E^{\prime}}^{2}-B^{\prime 2}=E^{2}-B^{2}$.

Step by Step Solution

★★★★★

3.46 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanics Questions!

In the previous problem, you derived the Lorentz transformations of the B field starting with the assumption that the scalar and vector potentials are components of a four vector \(A^{\mu}=(\phi,...

We discovered in the text that the scalar and vector potentials are components of a four vector $A^{\mu}=(\phi, \mathbf{A})$. In this problem, we will take as given the existence of this...

Consider two inertial frames $\mathcal{O}$ and $\mathcal{O}^{\prime}$ where $\mathcal{O}^{\prime}$ is moving with velocity $\mathbf{v}$ relative to $\mathcal{O}$. We split all three-vectors...

A train with proper length L moves at speed c/2 with respect to the ground. A ball is thrown from the back to the front, at speed c/3 with respect to the train. How much time does this take, and what...

Length contraction seems a bit self-contradictory in the example below: Example: A 125-meter-long train is moving at high speed of = 0.9 on a straight track passing through a garage of length 55 m...

Part 1: Matrix multiplication 1.1. Consider the following 3 x 3 matrices: 0 cos 3 - sin 3 0 COS O - sin o R. = sin 3 cos B 0 (1) sin a COS CK 0 0 which (as you will see next week, or you can check...

1. Problem-solving with Lorentz transformations. (a) (40 points) Solve Morin exercise 1.34 (p. 51) exclusively using Lorentz transformations; in other words, don't explicitly relate any lengths or...

Part 1: Boosts and rapidity For this part, we will need the definitions of the hyperbolic trig functions, sinh (pronounced "sinsh"), cosh (pronounced like it sounds), and tanh (pronounced "tansh"):...

1. Show that the Gallilean transformations leave the expression x2 + y? + z2 + cet invariant whereas the same expression is not invariant under Lorentz transformations. 2 Show that the Lorentz...

Q.1 Show that the Gallilean transformations leave the expression x + y + x + ct invariant whereas the same expression is not invariant under Lorentz transformations. Q.2 Show that the Lorentz...

The safety requirements for hard hats worn by construction workers and others, established by the American National Standards Institute (ANSI), specify that each of three hats pass the following...

Companies within the one world, Star, and Sky Team alliances have also engaged in major mergers and acquisitions (M&A): Frontier and US Air (Star), Delta and Northwest (Sky Team), and Continental and...

The FDO ( Franchisor Discloser Document ) contains 2 0 categories of information that give a prospective franchisee a broad base of informucion about the background and financial health of the...

Cartys Choices. Brian Carty, a prominent investor, is evaluating investment alternatives. If he believes an individual equity will rise in price from $59 to $71 in the coming one-year period, and the...

Recall that a C=C bond is comprised of a s bond and a p bond. These two bonds together have a combined BDE (bond dissociation energy) of 632 kJ/mol. Use this information to predict whether the...

Using acetylene and ethylene oxide as your only sources of carbon atoms, propose a synthesis for each of the following compounds. a. b.

Fill in the missing reagents below. Me OEt ?| Br Me SH OEt OMe OEt CN

1 Question 4: 18 marks 2 3 Bespoke Furniture Assemblers Inc. (BFAI) manufactures bedroom furniture in sets (a set includes a 4 dresser two queen-size beds, and one bedside table) for use in motels...

This trial balance of Wildhorse Co. does not balance. Each of the listed accounts has a normal balance per the general ledger. An examination of the ledger and journal reveals the following errors:...

Becton Labs, Inc., produces various chemical compounds for industrial use. One compound called Fludex, is prepared using an elaborate distilling process. The company has developed standard costs for...