Asked by Anonymous

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
Answered by FLu
a)0.197142857148
c)0.197142857148

b) any idea for this?
Answered by Anonymous
Formula, please Flu

and have you any part of Problems 1 and 2?
Answered by Phy
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
Answered by FLu
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?
Answered by Anonymous
Phy,
1 c,d
2 a,b
Answered by FLu
Anonymous, do you have 1 f?
Answered by Anonymous
No, Sorry.
Answered by FLu
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.
Answered by Anonymous
But 4th: (2)
dB eB both (E_0/c)*cos(pi/4)
Answered by FLu
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!
Answered by FLu
sorry meant some missing from Problem 1, 2 and 3 missing.
Answered by FLu
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?
Answered by Lex
Anyone please?
Answered by Phy
Thanks a lot Flu for the 4th prob

2nd prob-
a) Wavelength= 2*pi/k
Frequency= omega/(2*pi)
Answered by Phy
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
Answered by Phy
And can anyone tell me the answer of
1st (g)??
Answered by Phy
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?
Answered by P
I problem ans not coming right.
Answered by rohan
Q1 part f and part g formulae plz.....!
Answered by rohan
Q3 part b answer plz...!
Answered by rohan
neyone who has solved Q7 n Q8 ??
Answered by sat
Q1, f)? any ideas
Answered by sat
Q1, f)? any ideas
ThE PROBLEM IS WITH b0
Answered by FLu
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?
Answered by dude
question 3 i have no idea how to begin.
Answered by sat
Can someone help with SNELL'S LAW?
Answered by FLu
OK, got a) can you help with c) for second problem Phy?
maybe the value or formula.
Answered by Rohan
B0= E0/ speed of case 1 or case 2 u found in abuv parts !
Answered by P
Please tell Q1 e and b.
Answered by Rohan
neyone who has solved Q7 n Q8 ? Q3 part b , Q1 part g..........????
Answered by FLu
Rohan, is E_0=8.85418782*10^-12?

I don't get the result with the speed of case 1 and 2.
Answered by Rohan
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 ???
Answered by Rohan
neyone who has got the answer for Q8 part a and Q3 part b ?????
Answered by FLu
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?
Answered by FLu
Also somebody could help with Problem 2:
What is the value of k in radians per meter?
Answered by Lyn
B_0 in both cases seem difficult cannot get it, please help!
Answered by dude
Q3help!!
Answered by Anonymous
@ 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 ???
Answered by FLu
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.
Answered by FLu
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?
Answered by P
Pls tell ans of Q1 b,c,d,e,f,g
Answered by Ku
B_0 for Q1?
Answered by FLu
Did anyone got B_0 correct for Problem 1) f)?
Answered by Nae
PLease B_0 for Problem 1 both cases!
Answered by FLu
For B_0 the formula seems to be :
E_0/c
However, I cannot get the result. can anybody work with this or help?
Answered by P
Flu pls. tell ans of Q1 part b wavenumber, part c and e
Answered by P
Phy pls. tell ans of Q1 part b wavenumber, part c and e and 3b
Answered by Tani
Problem 3)b) please value or formula?
Answered by Mat
Help with Problem 3b please!
Answered by BoobleGum
wavenumber = (2*pi)/(Wavelength)
Answered by BoobleGum
it is analog W
Answered by Hard
BoobleGum can you help with Problem 3 b) please?
Answered by FLu
Anyone managed Problem 3) b) formula or value please?
Answered by P
Pls. tell ans of freq in Q1 and part e and g.
Answered by Nuyr
B_0 for Problem 3 please!?
Answered by BoobleGum
Hard, I didn't make Q3.

Give pliz somebody formulas on all questions from Q3 and explain as to find B_0 in Q1
Answered by Nur
Anyone for Q3 for B_0 both cases please!
Answered by Ronald
Please Problem 3 someone!?
Answered by Hur
Problem 3!
Answered by X10
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
Answered by FLu
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?
Answered by FLu
Meant value for b) X10 please?
Answered by FLu
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.
Answered by X10
Problem 1: part f: Bo= E_0/speed u got in case 1 or case2
Answered by j
formula for Q#8 part 1 or answer for α=84∘?
Answered by P
FLU pl tell ans for value t=2.4e-16
Answered by P
Pl tell ans for prob 1 part c case 2
1.6711e8 is showing wrong
Answered by FLu
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?
Answered by Hamed
X10 please tell value for 1)f)
how did you calculate step by step? having problems with solution
Answered by X10-Help
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?
Answered by gggg
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

Answered by G
for b
Answered by FLu
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!
Answered by Any
Anyone for 1)f) B_0 please?

formula didn't work, please help!
Answered by Maga
B_0 for 1)f) please?
Answered by Maga
is E_0=8.85418782*10^-12 value this?
It does not work with case 1/2 speed, please help!
Answered by X10
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)
Answered by FLu
No problem X10, thanks for it anyway!
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