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An electromagnetic wave of frequency $45 \mathrm{MHz}$ travels in free space along $X$-axis. At some point and at some instant, the electric field has a maximum value of $750 \mathrm{NC}^{-1}$ along $Y$-axis. The magnetic field at this position and time is
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Verified Answer
The correct answer is:
$2.5 \times 10^{-6} \hat{\mathbf{k}} \mathrm{T}$
Relation between electric and magnetic field in electromagnetic wave
$\begin{aligned}
& B=\frac{E}{c} \\
& E=750 \mathrm{~N} / \mathrm{C}
\end{aligned}$
Speed of light,
$\begin{aligned}
c & =3 \times 10^8 \mathrm{~m} / \mathrm{s} \\
B & =\frac{750}{3 \times 10^8} \\
B & =2.5 \times 10^{-6} \mathrm{~T}
\end{aligned}$
As, $B$ must be perpendicular to both $\mathbf{c}$ and $\mathbf{E}$, i.e.it is along $Z$-axis.
$B=2.5 \times 10^{-6} \hat{\mathbf{k}} \mathrm{T}$
$\begin{aligned}
& B=\frac{E}{c} \\
& E=750 \mathrm{~N} / \mathrm{C}
\end{aligned}$
Speed of light,
$\begin{aligned}
c & =3 \times 10^8 \mathrm{~m} / \mathrm{s} \\
B & =\frac{750}{3 \times 10^8} \\
B & =2.5 \times 10^{-6} \mathrm{~T}
\end{aligned}$
As, $B$ must be perpendicular to both $\mathbf{c}$ and $\mathbf{E}$, i.e.it is along $Z$-axis.
$B=2.5 \times 10^{-6} \hat{\mathbf{k}} \mathrm{T}$
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