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Electromagnetic Waves question

2019 · 12 Jan · Shift 2 · Q49
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Electromagnetic Waves question

2019 · 12 Jan · Shift 2 · Q49

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
The mean intensity of radiation on the surface of the Sun is about 108 W/m2 . The rms value of the corresponding magnetic field is closet to :
  1. A
    102 T
  2. B
    10 −-− 2 T
  3. C
    10 −-− 4 T
  4. D
    1 T
View written solutionFree

Correct answer: C

  1. For an electromagnetic wave, the average intensity is related to the rms fields by

I=cμ0Brms2I = \frac{c}{\mu_0} B_{\rm rms}^2I=μ0​c​Brms2​

where:

  • I=108 W/m2I = 10^8\ \text{W/m}^2I=108 W/m2
  • c=3×108 m/sc = 3 \times 10^8\ \text{m/s}c=3×108 m/s
  • μ0=4π×10−7 H/m\mu_0 = 4\pi \times 10^{-7}\ \text{H/m}μ0​=4π×10−7 H/m
  1. Solve for BrmsB_{\rm rms}Brms​:

Brms=Iμ0cB_{\rm rms} = \sqrt{\frac{I\mu_0}{c}}Brms​=cIμ0​​​

  1. Substitute values:

Brms=(108)(4π×10−7)3×108B_{\rm rms} = \sqrt{\frac{(10^8)(4\pi \times 10^{-7})}{3 \times 10^8}}Brms​=3×108(108)(4π×10−7)​​

=4π×1013×108= \sqrt{\frac{4\pi \times 10^{1}}{3 \times 10^8}}=3×1084π×101​​

=4π3×10−7= \sqrt{\frac{4\pi}{3} \times 10^{-7}}=34π​×10−7​

  1. Approximate numerically:

4π3≈4.19\frac{4\pi}{3} \approx 4.1934π​≈4.19

So,

Brms≈4.19×10−7B_{\rm rms} \approx \sqrt{4.19 \times 10^{-7}}Brms​≈4.19×10−7​

≈2.05×10−3.5\approx 2.05 \times 10^{-3.5}≈2.05×10−3.5

A better direct calculation:

Brms≈6.5×10−4 TB_{\rm rms} \approx 6.5 \times 10^{-4}\ \text{T}Brms​≈6.5×10−4 T

  1. Compare with options:
  • 102 T10^2\ \text{T}102 T : too large
  • 10−2 T10^{-2}\ \text{T}10−2 T : too large
  • 10−4 T10^{-4}\ \text{T}10−4 T : closest
  • 1 T1\ \text{T}1 T : too large

Hence the closest option is:

C (10−4 T)\boxed{\text{C } (10^{-4}\ \text{T})}C (10−4 T)​

  1. Verification with stored answer:
  • Derived answer: C
  • Stored correct answer: C
  • They agree.
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