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Determine, B0, ω, K, and λ. Find Expressions for E and B. - CBSE (Science) Class 12 - Physics

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Question

Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B0ω, k, and λ. (b) Find expressions for and B.

Solution

Electric field amplitude, E0 = 120 N/C

Frequency of source, ν = 50.0 MHz = 50 × 106 Hz

Speed of light, c = 3 × 10m/s

(a) Magnitude of magnetic field strength is given as:

`B_0=E_0/c`

`=120/(3xx10^8)`

`=4xx1)^-7 T=400 nT`

Angular frequency of source is given as:

ω = 2πν

= 2π × 50 × 106

= 3.14 × 108 rad/s

Propagation constant is given as:

`k=omega/c`

`=(3.14xx10^8)/(3xx10^8)=1.05 "rad"/m`

Wavelength of wave is given as:

`lambda=c/v`

`=(3xx10^8)/(50xx10^6)=6.0 m`

(b) Suppose the wave is propagating in the positive x direction. Then, the electric field vector will be in the positive y direction and the magnetic field vector will be in the positive z direction. This is because all three vectors are mutually perpendicular.

Equation of electric field vector is given as:

`vecE=E_0sin(kw-omegat)hatj`

`=120sin[1.05x-3.14xx10^8t]hatj`

And, magnetic field vector is given as:

`vecB=B_0sin(kx-omegat)hatk`

`vecB=(4xx10^-7)sin[1.05x-3.14xx10^8t]hatk`

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 8: Electromagnetic Waves
Q: 8 | Page no. 286

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Solution Determine, B0, ω, K, and λ. Find Expressions for E and B. Concept: Electromagnetic Waves.
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