Sunday

February 14, 2016
Posted by **Anonymous** on Saturday, May 11, 2013 at 11:22am.

E⃗ =E0xˆcos(kz−ωt),B⃗ =B0yˆcos(kz−ωt)

satisfy all 4 Maxwell's equations. In lectures, I showed that an application of the generalized Ampere's Law (closed loop surrounding area A2, see below), leads to: B0=ε0μ0cE0, and I mentioned that independently it follows from an application of Faraday's Law that B0=E0/c. Combining these two results then leads to the fantastic result that the “speed of light" in vacuum c=1/ε0μ0‾‾‾‾‾√. I want you to show that Faraday's Law indeed leads to the result B0=E0/c. You can show this by choosing a similar special area as we did in lectures:

We define the normal of the surface A1 in the figure above to point in the +yˆ direction. In the following , assume that ℓ=1 m, E0=1 V/m, f=610×1012 Hz, where f is the frequency of oscillation.

(a) We define f1(t)=∮E⃗ ⋅dℓ⃗ , where ∮E⃗ ⋅dℓ⃗ is the closed loop integral taken along the contour of the area A1 in the figure above. Evaluate the function f1(t) in Volts for the following value of t

t=2e-16 sec

(b) Consider the function f2(t)=ϕB(t). Following the method used in Lecture 27, calculate the function f2(t), and evaluate it (in Volts seconds) for the following time t

t=2e-16 sec

(c) Consider again the function f2(t) and evaluate −df2(t)dt in Volts for the following time t

t=2e-16 sec

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**FLu**, Sunday, May 12, 2013 at 10:48ama)0.197142857148

c)0.197142857148

b) any idea for this?

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**Anonymous**, Sunday, May 12, 2013 at 11:19amFormula, please Flu

and have you any part of Problems 1 and 2?

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**Phy**, Sunday, May 12, 2013 at 12:28pmWhat are the answers when t=2.2e-16??

And do u have answers for the 4th question?

Anonymous, I have the answers for the 1st and 2nd problems, can u tell me the specific questions for whom u want the answers

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**FLu**, Sunday, May 12, 2013 at 12:39pmSorry Anonymous, just put the numbers in I don't have the formula.

Problem 2:

a)?

b)1.5

c)First answer: (n*E_0)/c

d)all 0

Do you have a) and second and third answer for c) phy?

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**Anonymous**, Sunday, May 12, 2013 at 12:41pmPhy,

1 c,d

2 a,b

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**FLu**, Sunday, May 12, 2013 at 12:43pmAnonymous, do you have 1 f?

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**Anonymous**, Sunday, May 12, 2013 at 12:50pmNo, Sorry.

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**FLu**, Sunday, May 12, 2013 at 12:52pmNo prob Anonymous.

1)b) is 1.5 by the way, if you have slightly different values, make some guesses, it is normally around that value.

with other values it is the same, it must be around that.

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**Anonymous**, Sunday, May 12, 2013 at 12:52pmBut 4th: (2)

dB eB both (E_0/c)*cos(pi/4)

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**FLu**, Sunday, May 12, 2013 at 12:54pmThanks Anonymous I have all other just some part from 1, 2 and 2 missing.

If Phy or someone figures out please let us have it or the formula.

thanks!

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**FLu**, Sunday, May 12, 2013 at 12:55pmsorry meant some missing from Problem 1, 2 and 3 missing.

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**FLu**, Sunday, May 12, 2013 at 1:48pmPhy 4 Problem:

0

cos(pi/4)

cos(pi/4)

0

-(E_0/c)*cos(pi/4)

(E_0/c)*cos(pi/4)

0

cos(pi/4)

-cos(pi/4)

0

(E_0/c)*cos(pi/4)

(E_0/c)*cos(pi/4)

PHy can you give the remaining answers for Problem 1 and 2?

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**Lex**, Sunday, May 12, 2013 at 7:26pmAnyone please?

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**Phy**, Sunday, May 12, 2013 at 11:34pmThanks a lot Flu for the 4th prob

2nd prob-

a) Wavelength= 2*pi/k

Frequency= omega/(2*pi)

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**Phy**, Sunday, May 12, 2013 at 11:36pm1st prob-

c) 1.451e8 and

1.6711e8

d) 1.936e8 and

2.229e8

If you want answers of any other probs or formulas, please let me know

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**Phy**, Sunday, May 12, 2013 at 11:38pmAnd can anyone tell me the answer of

1st (g)??

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**Phy**, Sunday, May 12, 2013 at 11:40pmAnd Flu, from where did you find out the answers for 3rd prob?? My grader isn't accepting the the answer which u told, can u please tell me the formula, or from where u found out the answer?

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**P**, Monday, May 13, 2013 at 12:20amI problem ans not coming right.

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**rohan**, Monday, May 13, 2013 at 5:29amQ1 part f and part g formulae plz.....!

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**rohan**, Monday, May 13, 2013 at 6:02amQ3 part b answer plz...!

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**rohan**, Monday, May 13, 2013 at 6:10amneyone who has solved Q7 n Q8 ??

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**sat**, Monday, May 13, 2013 at 11:59amQ1, f)? any ideas

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**sat**, Monday, May 13, 2013 at 11:59amQ1, f)? any ideas

ThE PROBLEM IS WITH b0

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**FLu**, Monday, May 13, 2013 at 12:27pmPhy, sorry no formula, was an accident to get the value. But our values are not far off so try to guess a little it must be around my value.

Your value did not work for me too.

Could you tell me what the value for k and omega is please Phy?

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**dude**, Monday, May 13, 2013 at 12:58pmquestion 3 i have no idea how to begin.

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**sat**, Monday, May 13, 2013 at 1:58pmCan someone help with SNELL'S LAW?

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**FLu**, Monday, May 13, 2013 at 3:22pmOK, got a) can you help with c) for second problem Phy?

maybe the value or formula.

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**Rohan**, Monday, May 13, 2013 at 5:02pmB0= E0/ speed of case 1 or case 2 u found in abuv parts !

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**P**, Tuesday, May 14, 2013 at 12:27amPlease tell Q1 e and b.

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**Rohan**, Tuesday, May 14, 2013 at 4:16amneyone who has solved Q7 n Q8 ? Q3 part b , Q1 part g..........????

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**FLu**, Tuesday, May 14, 2013 at 9:13amRohan, is E_0=8.85418782*10^-12?

I don't get the result with the speed of case 1 and 2.

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**Rohan**, Tuesday, May 14, 2013 at 9:52amno ur eqn is of the form E= Eo(kx- wt), sooo u can guess nw ! okkay do u hav answers for Q3 part b, Q 1 part g n Q 8 ???

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**Rohan**, Tuesday, May 14, 2013 at 5:50pmneyone who has got the answer for Q8 part a and Q3 part b ?????

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**FLu**, Tuesday, May 14, 2013 at 7:14pmQ8)

a)0.89

b)1.34

Rohan, experiment with some guesses if it does not fit, as you can see the number is quite narrow.

I could not figure B_0 out but with your formula managed +-omega in both cases, can you help me with the formula please Rohan?

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**FLu**, Tuesday, May 14, 2013 at 7:20pmAlso somebody could help with Problem 2:

What is the value of k in radians per meter?

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**Lyn**, Tuesday, May 14, 2013 at 7:21pmB_0 in both cases seem difficult cannot get it, please help!

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**dude**, Wednesday, May 15, 2013 at 6:26amQ3help!!

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**Anonymous**, Wednesday, May 15, 2013 at 8:14am@ FLU :- Q8 1st part, I tried everythin but didnt get green tick, mine alpha angle is 70 degree and n=1.5

Also what is Q3 part b answer ???

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**FLu**, Wednesday, May 15, 2013 at 9:30amOK try for b) 1.5 as n was in my part the answer.

try for a) 0.60 and go up some decimals, 0.62.0.64 etc. it must be around that, because values are not very far away from that.

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**FLu**, Wednesday, May 15, 2013 at 9:32amQ3 part b I do not have yet, so if anyone has please help.

Do you have Q1) f) B_0 for both cases? value and/or formula Anonymous?

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**P**, Wednesday, May 15, 2013 at 9:53amPls tell ans of Q1 b,c,d,e,f,g

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**Ku**, Wednesday, May 15, 2013 at 2:34pmB_0 for Q1?

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**FLu**, Wednesday, May 15, 2013 at 5:59pmDid anyone got B_0 correct for Problem 1) f)?

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**Nae**, Wednesday, May 15, 2013 at 8:33pmPLease B_0 for Problem 1 both cases!

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**FLu**, Wednesday, May 15, 2013 at 8:38pmFor B_0 the formula seems to be :

E_0/c

However, I cannot get the result. can anybody work with this or help?

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**P**, Thursday, May 16, 2013 at 7:50amFlu pls. tell ans of Q1 part b wavenumber, part c and e

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**P**, Thursday, May 16, 2013 at 8:04amPhy pls. tell ans of Q1 part b wavenumber, part c and e and 3b

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**Tani**, Thursday, May 16, 2013 at 9:47pmProblem 3)b) please value or formula?

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**Mat**, Thursday, May 16, 2013 at 9:56pmHelp with Problem 3b please!

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**BoobleGum**, Friday, May 17, 2013 at 4:30amwavenumber = (2*pi)/(Wavelength)

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**BoobleGum**, Friday, May 17, 2013 at 4:31amit is analog W

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**Hard**, Friday, May 17, 2013 at 9:28amBoobleGum can you help with Problem 3 b) please?

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**FLu**, Friday, May 17, 2013 at 9:31amAnyone managed Problem 3) b) formula or value please?

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**P**, Friday, May 17, 2013 at 10:00amPls. tell ans of freq in Q1 and part e and g.

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**Nuyr**, Friday, May 17, 2013 at 10:13amB_0 for Problem 3 please!?

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**BoobleGum**, Friday, May 17, 2013 at 11:01amHard, I didn't make Q3.

Give pliz somebody formulas on all questions from Q3 and explain as to find B_0 in Q1

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**Nur**, Friday, May 17, 2013 at 11:47amAnyone for Q3 for B_0 both cases please!

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**Ronald**, Friday, May 17, 2013 at 11:48amPlease Problem 3 someone!?

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**Hur**, Friday, May 17, 2013 at 1:18pmProblem 3!

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**X10**, Friday, May 17, 2013 at 4:11pmPart a and Part c:

d/dt (l (sin((k lambda)/4-t omega)+sin(t omega)))/k where t=2.4*10^-16; omega=3.83*10^15; k=12775810.12; lambda=4.91*10^-7;l=1

Put this value in wolframalpha and divide the result by speed of light

and for Part b: Integrate[Cos[k z - omega t], {z, 0, lambda/4}, {x, 0, l}] where t=2.2*10^-16; omega=3.83*10^15; k=12775810.12; lambda=4.91*10^-7;l=1

Put this value in wolframalpha and divide the result by speed of light

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**FLu**, Friday, May 17, 2013 at 5:20pmMAny thanks X10! I dont sem to get the result. could you give ,e your value, so I can find an approximation for mine?

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**FLu**, Friday, May 17, 2013 at 5:26pmMeant value for b) X10 please?

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**FLu**, Friday, May 17, 2013 at 5:38pmGot it X10 thanks vey much!

can you maybe help with Problem 1) f) case 2? I cannot get the B_0 for case 2.

A formula and the value, I would be greatful.

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**X10**, Saturday, May 18, 2013 at 2:13amProblem 1: part f: Bo= E_0/speed u got in case 1 or case2

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**j**, Saturday, May 18, 2013 at 5:56amformula for Q#8 part 1 or answer for α=84∘?

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**P**, Saturday, May 18, 2013 at 7:44amFLU pl tell ans for value t=2.4e-16

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**P**, Saturday, May 18, 2013 at 8:01amPl tell ans for prob 1 part c case 2

1.6711e8 is showing wrong

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**FLu**, Saturday, May 18, 2013 at 10:24amThanks X10, have same problem like P.

I don't get it. is this the formula, my speed case value is:200500000

(8.85418782*10^-12)/(200500000)

Is there a mistake with my E_0 value?

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**Hamed**, Saturday, May 18, 2013 at 10:30amX10 please tell value for 1)f)

how did you calculate step by step? having problems with solution

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**X10-Help**, Saturday, May 18, 2013 at 12:13pmX10, the formula did not give a right answer, could you give us the value for yours? and is E_0= 8.85418782*10^-12?

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**gggg**, Saturday, May 18, 2013 at 1:56pmQ3 a,c (put your time)

-((3.83*10^15)/(2.99e8))*integral from 0 to ((4.91*10^-7)/4) of sin(12775810.12*z-3.83*10^15*2.6*10^-16) dz

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**G**, Saturday, May 18, 2013 at 2:08pmfor b

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**FLu**, Saturday, May 18, 2013 at 2:30pmgggg, for question 1)f) B_0 what is it the formula?

Could you give us the value, as the formula from X10 did not work for me.

thanks!

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**Any**, Saturday, May 18, 2013 at 3:01pmAnyone for 1)f) B_0 please?

formula didn't work, please help!

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**Maga**, Saturday, May 18, 2013 at 3:33pmB_0 for 1)f) please?

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**Maga**, Saturday, May 18, 2013 at 3:36pmis E_0=8.85418782*10^-12 value this?

It does not work with case 1/2 speed, please help!

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**X10**, Sunday, May 19, 2013 at 2:10amFLu sorry for late reply. My Internet not working for past 20 hrs. Anyhow I'm sorry for the time up. But the mistake u were doing is that E_o is ur maximum amplitude value in the given equation not permitivity constant.like in my case E_o= 55 in Ey=55sin(4.71x-1.09e10t)

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**FLu**, Sunday, May 19, 2013 at 11:07amNo problem X10, thanks for it anyway!