Electromagnetic WavesMedium
Question
A magnetic field vector in an electromagnetic wave is represented by, $\overrightarrow{B} = B_{0}sin\left( 2\pi vt - \frac{2\pi x}{\lambda} \right)\widehat{j}$. Its associated electric field vector is
Options
A.$\overrightarrow{E} = - v\lambda{\text{ }B}_{0}sin\left( 2\pi vt - \frac{2\pi x}{\lambda} \right)\widehat{k}$
B.$\overrightarrow{E} = - v\lambda{\text{ }B}_{0}sin\left( 2\pi vt - \frac{2\pi x}{\lambda} \right)\widehat{i}$
C.$\overrightarrow{E} = v\lambda{\text{ }B}_{0}sin\left( 2\pi vt - \frac{2\pi x}{\lambda} \right)\widehat{k}$
D.$\overrightarrow{E} = v\lambda{\text{ }B}_{0}sin\left( 2\pi vt - \frac{2\pi x}{\lambda} \right)\widehat{i}$
Solution
Sol. [Key Concept: The field unit vectors satisfy (E-dir)$\times$(B-dir)$=$(propagation dir); with $E_{0} = v\lambda\ B_{0}$, the field E points along $- k$.]
$${\widehat{E} \times \widehat{B} = \widehat{C} }{\widehat{B} = \widehat{j} }{\widehat{C} = \widehat{i} }{\therefore\widehat{E} = - \widehat{k} }{\frac{E_{0}}{{\text{ }B}_{0}} = C = v\lambda }{E_{0} = B \times v\lambda }$$
Create a free account to view solution
View Solution FreeMore Electromagnetic Waves Questions
A point light source emits E.M. waves in free space. A detector, placed at a distance of L m , measures the intensity as...The electric and magnetic field, associated with an e.m. wave, propagating along the +z-axis, be represented by...An electromagnetic wave in vacuum has the electric and magnetic fields , which are always perpendicular to each other. T...The electric field associated with an e.m. wave in vacuum is given by 40 cos (kz - 6 × 10-8t), where E, z and t are in v...The electric field in a plane electromagnetic wave is given by$E_{z} = 60cos\left( 5x + 1.5 \times 10^{9}t \right)V/m$.T...