Question

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10} Hz$ and its energy density is $1.02 \times 10^{-8} J / m ^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to $\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{ Nm ^{2}}{ C ^{2}}\right.$ and speed of light $\left.=3 \times 10^{8} ms ^{-1}\right):$

• A. $180 \,nT$
• B. $160 \,nT$
• C. $150\, nT$
• D. $190 \,nT$

Answer 1

Answer: (B)

Energy density $\frac{ dU }{ dV }=\frac{ B _{0}^{2}}{2 \mu_{0}}$
$1.02 \times 10^{-8}=\frac{ B _{0}^{2}}{2 \times 4 \pi \times 10^{-7}}$
$B _{0}^{2}=\left(1.02 \times 10^{-8}\right) \times\left(8 \pi \times 10^{-7}\right)$
$B _{0}=16 \times 10^{-8} T =160 nT$