Question

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.724 W/m2. What is the maximum value of the magnetic field in the wave? (c=3.0×108m/s, μ0=4π×10−7T⋅m/A, ε0=8.85×10−12C2/N⋅m2)

Answer 1

Answer:

The maximum value of the magnetic field in the wave is $7.79\times10^{-8}\ T.$

Explanation:

Given that,

Average value of pointing vector = 0.724 W/m²

We need to calculate the magnetic field

Using formula of pointing vector

$S=\dfrac{1}{\mu_{0}}(E\times B)$

The average value of pointing vector

$S=\dfrac{1}{2\mu_{0}}\times E_{0}B_{0}....(I)$

We know that,

$E_{0}=cB_{0}$

Put the value of $E_{0}$ in equation (II)

$S=\dfrac{1}{2\mu_{0}}\times c(B_{0})^2$

substitute the value in the formula

$0.724=\dfrac{1}{2\times4\pi\times10^{-7}}\times3\times10^{8}\times (B_{0})^2B_{0}=\sqrt{\dfrac{0.724\times2\times4\pi\times10^{-7}}{3\times10^{8}}}B_{0}=7.79\times10^{-8}\ T$

The maximum value of the magnetic field in the wave is $7.79\times10^{-8}\ T.$