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Verify that energy density can also be written as average Poynting flux divided by light speed.
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- What is the physical significance of the Poynting vector?The Poynting vector describes a flow of energy whenever electric and magnetic fields are present. Consider a long cylindrical wire of radius r with a current I in the wire, with resistance R and voltage V. From the expressions for the electric field along the wire and the magnetic field around the wire, obtain the magnitude and direction of the Poynting vector at the surface. Show that it accounts for an energy flow into the wire from the fields around it that accounts for the Ohmic heating of the wire.Let (50, 70, 1500) be the coordinate of a light source of intensity 0.95 units. The light is illuminating a sphere whose center is at C(10, -15, 6). Determine the intensity of the reflected light from a point P(20, 10, 120) on the sphere using a diffuse reflection model. Given that the diffuse absorption coefficient of the quad surface is 0.8 unit.
- Calculate the degree of polarization as a function of the angle θ between the incident radiation and the scattered radiation for Thompson scattering of unpolarized, monochromatic radiation.The electric field in a sine wave has a peak value of 32.6 mV/m. Calculate the magnitude of the Poynting vector in this case.2.4 Show that the average Poynting flux is given by the expression Re (Eo x H), where E. and Ho are the complex field ampli- tudes of a light wave.
- 8.4. Show that for dipole radiation with Ë = -c x B, B=; * Cos e 4TEqcr² the Poynting vector is Te sin? 0 . (4x)²ɛ0 r³ Give a physical interpretation for this result. In the case of a mobile phone, d points in the direction of the antenna. In which direction does most of the radiation go?A laser beam of intensity I reflects from a flat, totally reflecting surface of area A, with a normal at angle u with the beam.Write an expression for the beam’s radiation pressure pr(u) on the surface in terms of the beam’s pressure when u = 0degree.Two infinitely long parallel plates of width w are located at w distance apart,. The two plates behave as black surfaces, where surface 1 has a temperature of 500°C and surface 2 has a temperature of 50°C. Determine the radiation heat flux between the two surfaces.
- An LED with total power Ptot=910 mW emits UV light of wavelength 370 nm. Assuming the LED is 45% efficient and acts as an isotropic point source (i.e., emits light uniformly in all directions), what is the amplitude of the electric field, E0, at a distance of 2.5 cm from the LED?Discuss Poynting vector related to power flow in free space. A uniform plane wave at frequency of 200 MHz travel in vacuum along positive Y direction. The electric field at some instance is given as E=3ax+5az . Find the phase constant of the wave.Let E=(-2jŷ) e˜³², H =- (2 jî +ŷ) e¯jz 377 (a) Find the time-averaged Poynting's vector . (b) Find the instantaneous Poynting's vector (z,t). (c) Show that the results from (a) and (b) are consistent.