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 x 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/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)

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

Put the value into the formula

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

$B_{0}=\sqrt{\dfrac{0.724\times2\times4\pi\times10^{-7}}{3\times10^{8}}}$

$B_{0}=7.79\times10^{-8}\ T$

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