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If the total energy transferred to a surface in time t is 6.48 times 10^5 mathrm~J, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Solution & Explanation

### Related Formula p = fracUc ### Core Logic For an electromagnetic wave incident on a surface that is completely absorbed, the total momentum transferred is equal to the total energy transferred divided by the speed of light in vacuum (c). ### Step 1: Calculate Momentum Given total energy E = 6.48 times 10^5 mathrm~J. Speed of light c = 3 times 10^8 mathrm~m/s. p = fracEc = frac6.48 times 10^53 times 10^8 p = 2.16 times 10^-3 mathrm~kg~m/s ### Pattern Recognition Always check for "complete absorption" versus "perfect reflection". For complete absorption, p = E/c. For perfect reflection, p = 2E/c. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

Reference Study Guides

Electromagnetic Waves

More Electromagnetic Waves Previous-Year Questions — Page 5

Q40 jee_main_2024_31_jan_morning Energy Density Of EM Waves
In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 times 10^10 mathrm~Hz and an amplitude of 50 mathrm~Vm^-1. The total average energy density of the electromagnetic field of the wave is : [Use varepsilon_0 = 8.85 times 10^-12 \, textC^2 / textNm^2 ]
  • A. 1.106 times 10^-8 \, mathrmJm^-3
  • B. 4.425 times 10^-8 mathrm~Jm^-3
  • C. 2.212 times 10^-8 mathrm~Jm^-3
  • D. 2.212 times 10^-10 mathrm~Jm^-3

Solution

### Related Formula U_texttotal average = frac12epsilon_0 E_0^2 ### Core Logic For an electromagnetic wave, the total average energy density is the sum of the average energy density of the electric field and the magnetic field. They are equal, so: U_textavg = U_E + U_B = 2U_E = 2 left( frac14epsilon_0 E_0^2 right) = frac12epsilon_0 E_0^2 Where E_0 is the amplitude of the electric field. ### Step 2: Substitution Given: E_0 = 50 mathrm\, V/m epsilon_0 = 8.85 times 10^-12 mathrm\, C^2/(Ncdot m^2) U_textavg = frac12 times (8.85 times 10^-12) times (50)^2 U_textavg = frac12 times 8.85 times 10^-12 times 2500 U_textavg = 1.10625 times 10^-8 mathrm\, J/m^3 ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

More Electromagnetic Waves Questions — jee_main_2024_30_january_evening

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