The electric field a plane electromagnetic wave is given by : E_y = 69 sin [ 0.6 times 10^3 x - 1.8 times 10^11 t ]text V/m. The expression for magnetic field associated with this electromagnetic wave is ____ T.

Solution & Explanation

### Related Formula B_0 = fracE_0c hatc = hatE times hatB ### Core Logic The phase of the wave is (0.6 times 10^3 x - 1.8 times 10^11 t). This indicates the wave propagates in the +x direction, so hatc = hati. The electric field oscillates along the y-axis, so hatE = hatj. From hatB = hatc times hatE, we have hatB = hati times hatj = hatk. So, the magnetic field is along the z-axis (B_z). ### Step 1: Calculate Amplitude of B Wave speed v = c = fracomegak = frac1.8 times 10^110.6 times 10^3 = 3 times 10^8text m/s. The amplitude of the magnetic field is: B_0 = fracE_0c = frac693 times 10^8 = 23 times 10^-8 = 2.3 times 10^-7text T The phase remains exactly the same as the electric field: B_z = 2.3 times 10^-7 sin(0.6 times 10^3 x - 1.8 times 10^11 t) ### Pattern Recognition B_0 = E_0/c gives the magnitude. The vector identity hatB = hatv times hatE gives the direction. Phase part never changes sign or terms between E and B equations. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

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Electromagnetic Waves

More Electromagnetic Waves Previous-Year Questions — Page 5

Q40 jee_main_2024_31_jan_evening Properties of EM Waves
Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:
  • A. Statement I is incorrect but Statement II is correct
  • B. Both Statement I and Statement II are correct
  • C. Both Statement I and Statement II are incorrect
  • D. Statement I is correct but Statement II is incorrect

Solution

### Related Formula rho_E = frac12varepsilon_0 E_rms^2 rho_B = fracB_rms^22mu_0 p_r = fracIc (radiation pressure for completely absorbing surface) ### Core Logic Statement I: In an EM wave, energy is stored in both the electric and magnetic fields. The energy densities are equal: U_E = U_B because E = cB and c^2 = frac1mu_0 epsilon_0. This is a correct fact. Statement II: Electromagnetic waves carry momentum (p = U/c). When they strike a surface, they transfer this momentum, creating radiation pressure. This is also a correct fact. ### Step 1: Final Evaluation Since both facts are universally true theoretical properties of EM waves, both statements are correct. ### Pattern Recognition Standard NCERT theory. Energy density is strictly symmetric 50-50 between E and B. Momentum transfer to pressure is the definitive signature of the particle-like nature (photons) of EM waves. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves
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

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