A complex number A is written as A = a+ib Rewrite A in polar from, [A|e¬i® and of course find [A| and o in terms of a and b.
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Q: A number N of plane waves are travelling parallel; the waves share a common wavevector k and common…
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Q: (6) Work out the commutation relation: Î,f|
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Q: (5) Work out the commutation relation:
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Q: Work out the commutation relation:
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Q: A number N of plane waves are travelling parallel; the waves share a common wavevector k and common…
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Q: Consider a sinusoidal electromagnetic wave of the form Ex = c * By = E0 * sin [2 * pi * f * (t -…
A: The final answer is attached below Explanation:
Given,
Simplifying we have,
Thus,
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- Problem 1. In class we will consider the sum of the electric field of two plane waves, u:(z.t) and uz(z.t), both traveling in the positive z direction with slightly different frequencies and propagation constants and with equal amplitudes. The electric fields of both plane waves are oriented in the y direction, which means that they have the same "polarization". The time and space variation of the two electric fields are given by: u: (2.1) = cos(@t - kz) uz(2.1) = cos ([o + Ao]t - [k + Ak]2) We will show that the sum of these two waves produce an intensity envelope in time and space that modulates the carrier frequency of m + Ao/2. The velocity of the envelope is called the group velocity. Assume Ao is << than o. For this problem, consider the sum of two slightly different waves with similar electric fields: v.(z) = sin(ot - kz) vz(z1) = sin([o + Ao]t - [k + Ak]z) Derive analytically an expression for a) the group and b) the phase velocity for the sum of the two fields. HINT: sinfa) +…In free space, let H= 89(106)/p sinpâp. UNDERSTAND and SOLVE Maxwell's equations to CALCULATE the flux crossing the surface defined by 0< p < n/3, 0 < z< 2mhow to find the normalisation constant please?
- Solve the partial differential equation 2² 8² da? (x, y) + dy² V(x, y) = 0 using the separattion of variables technique for partial differential equations. That is, let (x, y) = f(x)g(y) and obtain two ordinary differential equations, one for f(x) and the other for g(y). Choose your separation constant to be k². Then, obtain the general solution to each of the ordinary differential equations. Finally, obtain the general solution for (x, y).A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eo and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by E₁ = Eoiû Re [exp j(k-r - wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec|² 27⁰ where the complex amplitude E, is defined by Inet and 70 is the impedance of free space. N Ec = Eoi exp(joi), 7 i=1(1) Derive the Maxwell's relations ƏT as, S V Əs \ƏT. T V G), = - aT T