MYTUTOR SUBJECT ANSWERS

295 views

Show Maxwell's equations in free space satisfy the wave equation

Maxwell's equations in free space:

∇ . E = 0

= -B/t

∇ . B = 0

∇ B = (1/c2)(∂E/t)

The wave equation: 

2(1/c2)(2U/t2)

If we take the curl of ∇ E, we get ∇ x(∇ E) = -(/t)∇ B

Using the vector formula a×(b×c) = b(a· c)−c(a·b), we can expand the left hand side to: ∇(∇ . E) - E(∇.∇)

Since ∇.E = 0, this becomes -2-(/t)∇ B

As ∇ B = (1/c2)(∂E/t), we have -2-(/t)(1/c2)(∂E/t)

Thus, 2(1/c2)(2E/t2) which shows that Maxwell's equations satisfy the wave equation. A similar process can be applied to B

Dojcin D. GCSE Physics tutor, A Level Chemistry tutor, GCSE Chemistry...

2 years ago

Answered by Dojcin, an A Level Physics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

47 SUBJECT SPECIALISTS

£22 /hr

Jonathan P.

Degree: Physics (Masters) - Durham University

Subjects offered: Physics, Maths

Physics
Maths

“About Me: I am a Physics student at Durham University. My passion is physics, and by association maths, I will aim to instil asimilar passion in students during my tutorials. I am a highly patient and approachable individual.  I have...”

£20 /hr

Mohammad M.

Degree: General Engineering (Bachelors) - Durham University

Subjects offered: Physics, Maths+ 2 more

Physics
Maths
Chemistry
Arabic

“I am studying Engineering at Durham University. From a very early age I have been fascinated by machines; how they work, how they have developed over time, and how they are useful in society today. I have a keen interest in motors and ...”

MyTutor guarantee

£20 /hr

Ben A.

Degree: Medicine (Bachelors) - University College London University

Subjects offered: Physics, Maths+ 6 more

Physics
Maths
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“Hello,I am a first year medical student at University College London, When I was in sixth form, I helped tutor the younger years and I always enjoyed it, so I decided to keep it on in my university years.My subjects are the three m...”

About the author

Dojcin D.

Currently unavailable: no new students

Degree: Physics with Medical Physics (Bachelors) - Cardiff University

Subjects offered: Physics, Science+ 2 more

Physics
Science
Maths
Chemistry

“I was one of you not too long ago. Studying physics and teaching piano allows me to teach a wide variety of people in a number of ways, helping you get where you want to be, especially in the sciences.”

MyTutor guarantee

You may also like...

Posts by Dojcin

Derive I = nAVe

Show Maxwell's equations in free space satisfy the wave equation

Other A Level Physics questions

A ball is thrown out of a window 18m off the ground. It is thrown horizontally at 0.5m/s. Show that it takes about 2s to reach the ground

Resolving the forces for an object suspended on two strings.

In still air an aircraft flies at 200 m/s . The aircraft is heading due north in still air when it flies into a steady wind of 50 m/s blowing from the west. Calculate the magnitude and direction of the resultant velocity?

Describe the photoelectric effect.

View A Level Physics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok