E = Eo sin(1200πt - βz)ax H= (Eo / η)*sin(1200πt- βz)az
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- A plane wave is propagating at a frequency of 100 MHz in a lossy medium. The amplitude of the electric field E at z=0 is equal to 200V/m. The medium is characterized by u=1 and &=2. 1. Find the propagation constant y after 1m: the amplitude of E loses 60% of its value and the its phase angle changes of 180'. 2. Find the conductivity a 3. Find the real and complex notations of the electric field 4. Find the expression of the magnetic field H 5. Deduce D and B 6. Find the expression of the Poyting vector 7. Find its average with respect to t.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) +…Genesis gets accepted to a Dental School in Idaho and when she arrives,she cannot find good signål. To fix this problem,Genesis orders a 2m long antenna on Amazon, and ottaches it to her phone.If the antenna carries a 900 mC chorge, what will be the force (mognitude and direction) on a 5 MC that is 30 cm (0.3)away from its Center? You have to derive the equation for the Electric field.
- Explain the answer to the second and last equation in detailIf electric and magnetic field strengths vary sinusoidally in time, being zero at t=0, then E=E0 sin 2πft and B=B0 Sin 2πft . Let f = 1.00 GHz here When do they reach their most negative value?Assuming the energy density of the cosmic background radiation of the Big Bang has the value 3.75 ✕ 10−14 J/m3, what is the corresponding electric field amplitude (in mV/m)?
- A parallel‑plate capacitor has closely spaced plates. Charge is flowing onto the positive plate and off of the negative plate at the rate of i=delta q/ delta t =2.5 A. What is the displacement current i(d) through the capacitor between the plates? i(d) = ?AAn electric field in a vacuum is determined to be polarized in the +y-direction. It has a peak of 250 μV/m at z = 0, and the next peak is at z = 5 cm. Determine phase velocity, propagation constant, wavelength, period, frequency, and radial frequency for this wave and write a complete function for e(z,t). Complete Solution pleaseProblem 8: In electromagnetic scattering by an infinite cylinder of radius a, under certain conditions, the time-harmonic electric field is given by E = u(p, ø) î, where u satisfies the Helmholtz wave equation 1 ди 1 02u + k?u = 0, 0 < 0< 27 0