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Question: Answered & Verified by Expert
A radio transmitter transmits at $830 \mathrm{kHz}$. At a certain distance from the transmitter magnetic field has amplitude $4.82 \times 10^{-11} \mathrm{~T}$. The electric field and the wavelength are respectively
PhysicsElectromagnetic WavesJEE MainJEE Main 2012 (26 May Online)
Options:
  • A
    $0.014 \mathrm{~N} / \mathrm{C}, 36 \mathrm{~m}$
  • B
    $0.14 \mathrm{~N} / \mathrm{C}, 36 \mathrm{~m}$
  • C
    $0.14 \mathrm{~N} / \mathrm{C}, 360 \mathrm{~m}$
  • D
    $0.014 \mathrm{~N} / \mathrm{C}, 360 \mathrm{~m}$
Solution:
2264 Upvotes Verified Answer
The correct answer is:
$0.014 \mathrm{~N} / \mathrm{C}, 360 \mathrm{~m}$
Frequency of EM wave $v=830 \mathrm{KHz}$ $=830 \times 10^3 \mathrm{~Hz}$.
Magnetic field, $B=4.82 \times 10^{-11} \mathrm{~T}$
As we know, frequency, $v=\frac{c}{\lambda}$
$$
\begin{aligned}
\text { or } \lambda & =\frac{c}{v}=\frac{3 \times 10^8}{830 \times 10^3} \\
\lambda & \simeq 360 \mathrm{~m} \\
\text { And, } E & =B C=4.82 \times 10^{-11} \times 3 \times 10^8 \\
& =0.014 \mathrm{~N} / \mathrm{C}
\end{aligned}
$$

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