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question_answer1) A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x - direction. At a particular point in space and time, \[\overrightarrow{E}=6.3\hat{j}V/m.\] The corresponding magnetic field \[\overrightarrow{B}\], at that point is \[x\times {{10}^{-\,8}}\hat{k}\,T\]. Find the value of x.
question_answer2) If the magnetic field of a plane electromagnetic wave is given by (The speed of light\[=3\times {{10}^{8}}m/s)\] \[B=100\times {{10}^{-6}}\sin \left[ 2\pi \times 2\times {{10}^{15}}\left( t-\frac{x}{c} \right) \right]\] then the maximum electric field (in N/C) associated with it is:
question_answer3) A 27 mW laser beam has a cross-sectional area of \[10\text{ }m{{m}^{2}}.\] The magnitude of the maximum electric field (in kV/m) in this electromagnetic wave is given by: [Given permittivity of space \[{{\in }_{0}}=9\times {{10}^{-12}}\] SI units. Speed of light \[c=3\times {{10}^{8}}m/s]\]
question_answer4) The mean intensity of radiation on the surface of the Sun is about \[{{10}^{8}}W/{{m}^{2}}\]. The rms value of the corresponding magnetic field (in tesla) is:
question_answer5) The magnetic field of a plane electromagnetic wave is given by: \[\overrightarrow{B}={{B}_{0}}\hat{i}[cos(kz-\omega t)]+{{B}_{1}}\hat{j}cos(kz+\omega t)\] Where \[{{B}_{0}}=3\times {{10}^{-5}}T\] and \[{{B}_{1}}=2\times {{10}^{-6}}T.\] The rms value of the force (in newton) experienced by a stationary charge \[Q={{10}^{-4}}C\] at \[Z=0\] is:
question_answer6) \[50\text{ }W/{{m}^{2}}\]energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy (25%) is reflected from the surface and the rest is absorbed. The force (in newton) exerted on \[1{{m}^{2}}\] surface area will be\[\left( c=3\times \text{1}{{\text{0}}^{8}}\text{ }m/s \right)\]:
question_answer7) A light beam travelling in the x - direction is described by the electric field \[{{E}_{y}}=300\sin \] \[\omega \left( t-\frac{x}{c} \right)\]. An electron is constrained to move along the y - direction with a speed of \[2.0\times {{10}^{7}}m/s.\] Find the maximum electric force (in newton) on the electron.
question_answer8) A laser beam has intensity \[2.5\times {{10}^{14}}\frac{W}{{{m}^{2}}}\]. Find the amplitude of electric field (in V/m) in the beam.
question_answer9) Light is incident normally on a completely absorbing surface with an energy flux of \[25\text{ }Wc{{m}^{-2}}.\] If the surface has an area of \[25c{{m}^{2}},\] the momentum (in Ns) transferred to the surface in 40 min time duration will be:
question_answer10) In a wave \[{{E}_{0}}=100\text{ }V{{m}^{-1}}.\] Find the magnitude of Poynting's vector in watt \[{{m}^{-2}}\].
question_answer11) The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength \[\left( in\text{ }volt\text{ }{{m}^{-1}} \right)\] is
question_answer12) A new system of unit is evolved in which the values of \[{{\mu }_{0}}\] and \[{{\in }_{0}}\] are 2 and 8 respectively. Then the speed of light in this system will be
question_answer13) A plane electromagnetic wave of wave intensity \[10W/{{m}^{2}}\] strikes a small mirror of area \[20\text{ }c{{m}^{2}}\], held perpendicular to the approaching wave. The radiation force (in newton) on the mirror will be
question_answer14) Radiations of intensity \[0.5\text{ }W/{{m}^{2}}\]are striking on a perfectly reflecting metal plate. The pressure \[\left( in\text{ }N/{{m}^{2}} \right)\]on the plate is
question_answer15) The electric field associated with an e.m. wave in vacuum is given by \[\overrightarrow{E}=\hat{i}40cos\left( kz-6\times {{10}^{8}}t \right),\]where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector \[k\] \[\left( in\text{ }metr{{e}^{-1}} \right)\] is
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