Electromagnetic Waves as Sinusoidal Waves Video Lessons

Concept

# Problem: At one instant the electric and magnetic fields at one point of an electromagnetic wave are E=(25i + 350j-50k) V/m and B = B0(7.2i-7.0j+ak)?TWhat is the value of B0?

###### FREE Expert Solution

3D vector magnitude:

$\overline{)|\stackrel{⇀}{E}|{=}\sqrt{{{E}_{\mathbit{x}}}^{2}+{{E}_{\mathbit{y}}}^{2}+{{E}_{\mathbit{z}}}^{2}}}$

Speed of light:

$\overline{){\mathbf{c}}{\mathbf{=}}\frac{\mathbf{E}}{\mathbf{B}}}$

The magnitude of the electric field:

$\begin{array}{rcl}\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbf{E}}\mathbf{|}& \mathbf{=}& \sqrt{{{\mathbf{E}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{E}}_{\mathbf{y}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{E}}_{\mathbf{z}}}^{\mathbf{2}}}\\ & \mathbf{=}& \sqrt{{\mathbf{\left(}\mathbf{25}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}{\mathbf{\left(}\mathbf{350}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}{\mathbf{\left(}\mathbf{-}\mathbf{50}\mathbf{\right)}}^{\mathbf{2}}}\end{array}$

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###### Problem Details

At one instant the electric and magnetic fields at one point of an electromagnetic wave are E=(25i + 350j-50k) V/m and B = B0(7.2i-7.0j+ak)?T

What is the value of B0?