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

a)0.197142857148

c)0.197142857148

b) any idea for this?

Formula, please Flu

and have you any part of Problems 1 and 2?

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

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?

Phy,

1 c,d
2 a,b

Anonymous, do you have 1 f?

No, Sorry.

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.

But 4th: (2)

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

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!