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March 28, 2017

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We discussed in lectures that traveling Electromagnetic waves in vacuum of the form
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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    a)0.197142857148
    c)0.197142857148

    b) any idea for this?

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    Formula, please Flu

    and have you any part of Problems 1 and 2?

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    What 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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    Sorry 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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    Phy,
    1 c,d
    2 a,b

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    Anonymous, do you have 1 f?

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    No, Sorry.

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    No 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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    But 4th: (2)
    dB eB both (E_0/c)*cos(pi/4)

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    Thanks 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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    sorry meant some missing from Problem 1, 2 and 3 missing.

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    Phy 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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    Anyone please?

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    Thanks a lot Flu for the 4th prob

    2nd prob-
    a) Wavelength= 2*pi/k
    Frequency= omega/(2*pi)

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    1st 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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    And can anyone tell me the answer of
    1st (g)??

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    And 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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    I problem ans not coming right.

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    Q1 part f and part g formulae plz.....!

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    Q3 part b answer plz...!

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    neyone who has solved Q7 n Q8 ??

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    Q1, f)? any ideas

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    Q1, f)? any ideas
    ThE PROBLEM IS WITH b0

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    Phy, 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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    question 3 i have no idea how to begin.

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    Can someone help with SNELL'S LAW?

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    OK, got a) can you help with c) for second problem Phy?
    maybe the value or formula.

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    B0= E0/ speed of case 1 or case 2 u found in abuv parts !

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    Please tell Q1 e and b.

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    neyone who has solved Q7 n Q8 ? Q3 part b , Q1 part g..........????

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    Rohan, 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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    no 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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    neyone who has got the answer for Q8 part a and Q3 part b ?????

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    Q8)
    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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    Also somebody could help with Problem 2:
    What is the value of k in radians per meter?

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    B_0 in both cases seem difficult cannot get it, please help!

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    Q3help!!

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    @ FLU :- Q8 1st part, I tried everythin but didn't get green tick, mine alpha angle is 70 degree and n=1.5

    Also what is Q3 part b answer ???

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    OK 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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    Q3 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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    Pls tell ans of Q1 b,c,d,e,f,g

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    B_0 for Q1?

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    Did anyone got B_0 correct for Problem 1) f)?

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    PLease B_0 for Problem 1 both cases!

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    For 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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    Flu pls. tell ans of Q1 part b wavenumber, part c and e

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    Phy pls. tell ans of Q1 part b wavenumber, part c and e and 3b

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    Problem 3)b) please value or formula?

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    Help with Problem 3b please!

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    wavenumber = (2*pi)/(Wavelength)

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    it is analog W

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    BoobleGum can you help with Problem 3 b) please?

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    Anyone managed Problem 3) b) formula or value please?

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    Pls. tell ans of freq in Q1 and part e and g.

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    B_0 for Problem 3 please!?

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    Hard, 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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    Anyone for Q3 for B_0 both cases please!

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    Please Problem 3 someone!?

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    Problem 3!

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    Part 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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    MAny thanks X10! I don't sem to get the result. could you give ,e your value, so I can find an approximation for mine?

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    Meant value for b) X10 please?

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    Got 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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    Problem 1: part f: Bo= E_0/speed u got in case 1 or case2

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    formula for Q#8 part 1 or answer for α=84∘?

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    FLU pl tell ans for value t=2.4e-16

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    Pl tell ans for prob 1 part c case 2
    1.6711e8 is showing wrong

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    Thanks 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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    X10 please tell value for 1)f)
    how did you calculate step by step? having problems with solution

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    X10, 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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    Q3 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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    for b

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    gggg, 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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    Anyone for 1)f) B_0 please?

    formula didn't work, please help!

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    B_0 for 1)f) please?

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    is E_0=8.85418782*10^-12 value this?
    It does not work with case 1/2 speed, please help!

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    FLu 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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    No problem X10, thanks for it anyway!

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