Q. 42 At one instant, the electric and... [FREE SOLUTION]

91影视

Chapter 31: Q. 42 (page 903)

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are $\overset{鈫�}{E} = (200 \hat{谋} + 300 \hat{确} - 50 \hat{k}) V / m$ and $\overset{鈫�}{B} = B_{0} (7.3 \hat{谋} - 7.3 \hat{确} + a \hat{k}) 渭 T$ .
a. What are the values of $a$ and $B_{0}$ ?
b. What is the Poynting vector at this time and position?

Short Answer

Expert verified

(a) The values of $a = - 14.6$ and $B_{o} = 6.7856 脳 10^{- 2}$

(b) The Poynting vector at time and position is $\overset{鈫�}{S} = - 260 \hat{i} + 140 \hat{j} - 200 \hat{k} W / m^{2}$

Step by step solution

Find a (part a)

By, $\overset{鈫�}{E} 鈯� \overset{鈫�}{B}$ :

$\overset{鈫�}{E} 脳 \overset{鈫�}{B} = 0$

$0 = (200) (7.3) + (300) (- 7.3) + (- 50) a$

$0 = 1460 + (- 2190) - 50 a$

$50 a = - 730$

$a = \frac{- 730}{50}$

$a = - 14.6$

Find Bo (part a)

$| \overset{鈫�}{E} | = c | \overset{鈫�}{B} |$

$((200)^{2}) + (300)^{2} + (50)^{2} = B_{o}^{2} {(3 脳 10^{8} m / s)}^{2} ((7.3)^{2} + (- 7.3)^{2} + (- 14.6)^{2})$

$B_{o}^{2} = \frac{((200)^{2}) + (300)^{2} + ((50)^{2})}{{(3 脳 10^{8} m / s)}^{2} ((7.3)^{2} + (- 7.3)^{2} + (- 14.6)^{2})}$

$B_{o} = \sqrt{\frac{((200)^{2}) + (300)^{2} + (50)^{2}}{{(3 脳 10^{8} m / s)}^{2} ((7.3)^{2} + (- 7.3)^{2} + (- 14.6)^{2})}}$

$B_{o} = 6.76 脳 10^{- 2}$

Find the Poynting vector

The Poynting vector is:

$\overset{鈫�}{S} = 渭_{o}^{- 1} \overset{鈫�}{E} 脳 \overset{鈫�}{B}$

$\overset{鈫�}{S} = 渭_{o}^{- 1} B_{o} (10^{- 6}) \{\begin{cases} [(300) (- 14.6) - (- 7.3) (- 50)] \hat{i} \\ + [(- 50) (7.3) - (- 14.6) (200)] \hat{j} \\ + [(200) (- 7.3) - (7.3) (300)] \hat{k} \end{cases}$

$\overset{鈫�}{S} = 渭_{o}^{- 1} B_{o} (10^{- 3}) [- 4.75 \hat{i} + 2.56 \hat{j} - 3.65 \hat{k}]$

$\overset{鈫�}{S} = - 260 \hat{i} + 140 \hat{j} - 200 \hat{k} W / m^{2}$

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

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Find a (part a)

Find Bo (part a)

Find the Poynting vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Modern Physics

Nuclear Physics

Conservation of Energy and Momentum

Famous Physicists

Space Physics

Study anywhere. Anytime. Across all devices.

91影视

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E鈫�=(200谋^+300确^-50k^)V/mand B鈫�=B0(7.3谋^-7.3确^+ak^)渭T. a. What are the values of aand B0? b. What is the Poynting vector at this time and position?

Short Answer

Step by step solution

Find a (part a)

Find Bo (part a)

Find the Poynting vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Modern Physics

Nuclear Physics

Conservation of Energy and Momentum

Famous Physicists

Space Physics

Study anywhere. Anytime. Across all devices.