Irodov Solutions → Oscillations and waves → Electromagnetic Waves. Radiation

4.189. An electromagnetic wave of frequency ν = 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity ε = 4.0. Find the increment of its wavelength.
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4.191. A plane electromagnetic wave of frequency ν = 10 MHz propagates in a poorly conducting medium with conductivity σ = 10 mS/m and permittivity ε = 9. Find the ratio of amplitudes of conduction and displacement current densities.
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4.192. A plane electromagnetic wave E = E_m cos(ωt - kr) propagates in vacuum. Assuming the vectors E_m and k to be known, find the vector H as a function of time t at the point with radius vector r = 0.
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4.193. A plane electromagnetic wave E = E_m cos(ωt - kr), where E_m = E_me_y, k = ke_x, e_x, e_y are the unit vectors of the x, y axes, propagates in vacuum. Find the vector H at the point with radius vector r = xe_x at the moment
(a) t = 0,
(b) t = t₀.
Consider the case when E_m = 160 V/m, k = 0.51 m^-1, x = 7.7 m, and t₀ = 33 ns.
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4.196. Find the mean Poynting vector <S> of a plane electromagnetic wave E = E_m cos(ωt - kr) if the wave propagates in vacuum.
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4.199. A standing electromagnetic wave with electric component E = E_m cos kx * cos ωt is sustained along the x axis in vacuum. Find the magnetic component of the wave B(x, t). Draw the approximate distribution pattern of the wave's electric and magnetic components (E and B) at the moments t = 0 and t = T/4, where T is the oscillation period.
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4.201. A parallel-plate air capacitor whose electrodes are shaped as discs of radius R = 6.0 cm is connected to a source of an alternating sinusoidal voltage with frequency ω = 1000 s^-1. Find the ratio of peak values of magnetic and electric energies within the capacitor.
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4.202. An alternating sinusoidal current of frequency ω = 1000 s^-1 flows in the winding of a straight solenoid whose cross-sectional radius is equal to R = 6.0 cm. Find the ratio of peak values of electric and magnetic energies within the solenoid.
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4.207. Fig. 4.39 illustrates a segment of a double line carrying direct current whose direction is indicated by the arrows. Taking into account that the potential φ₂ > φ₁, and making use of the Poynting vector, establish on which side (left or right) the source of the current is located.
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4.209. A source of ac voltage V = V₀ cos ωt delivers energy to a consumer by means of a long straight coaxial cable with negligible active resistance. The current in the circuit varies as I = I₀ cos (ωt - φ). Find the time-averaged energy flux through the cross-section of the cable. The sheath is thin.
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4.212. Find the mean radiation power of an electron performing harmonic oscillations with amplitude a = 0.10 nm and frequency ω = 6.5*10¹⁴ s^-1.
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