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A plane electromagnetic wave of frequency $25 \;MHz$ travels in free space along the $x$ -direction. At a particular point in space and time, $E = 6.3\,\hat j\;\,V/m$. What is $B$ at this point?
$1.9 \times 10^{-8}\;\hat i\;T$
$2.1 \times 10^{-8}\;\hat k\;T$
$2.1 \times 10^{-8}\;\hat j\;T$
$8.2 \times 10^{-8}\;\hat k\;T$
Solution
A plane electromagnetic wave of frequency $25 \;MHz$ travels in free space along the $x$ -direction. At a the magnitude of $B$ is
$B=\frac{E}{c}$
$=\frac{6.3 V / m }{3 \times 10^{8} m / s }=2.1 \times 10^{-8} T$
To find the direction, we note that $E$ is along $y$ -direction and the wave propagates along $x$ -axis. Therefore, $B$ should be in a direction perpendicular to both $x$ – and $y$ -axes. Using vector algebra, $E \times B$ should be along $x$ -direction. since, $( + \hat j) \times ( + \hat k) = \hat i$, $B$ is along the $z$ -direction. Thus,
$\quad B=2.1 \times 10^{-8}\;\hat k\;T$
