Electromagnetic Waves

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (U_e) and magnetic (U_m) fields is :

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, $$\overrightarrow B = 2.0 \times {10^{ - 8}}\widehat kT$$. (where, $$\widehat k$$ is unit vector along z-direction) What is $$\overrightarrow E$$ at this point?

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $$\left( {\overrightarrow E } \right)$$ and magnetic field $$\left( {\overrightarrow B } \right)$$ components.

In an electromagnetic wave the electric field vector and magnetic field vector are given as $$\overrightarrow E = {E_0}\widehat i$$ and $$\overrightarrow B = {B_0}\widehat k$$ respectively. The direction of propagation of electromagnetic wave is along :

The relative permittivity of distilled water is 81. The velocity of light in it will be : (Given $$\mu$$_r = 1)

A light beam is described by $$E = 800\sin \omega \left( {t - {x \over c}} \right)$$. An electron is allowed to move normal to the propagation of light beam with a speed of 3 $$\times$$ 10⁷ ms^$$-$$1. What is the maximum magnetic force exerted on the electron?

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $$-$$ 10 $$\times$$ 10¹⁰ t) V/m The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)

The magnetic field vector of an electromagnetic wave is given by $$B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t)$$; where $$\widehat i,\widehat j$$ represents unit vector along x and y-axis respectively. At t = 0s, two electric charges q₁ of 4$$\pi$$ coulomb and q₂ of 2$$\pi$$ coulomb located at $$\left( {0,0,{\pi \over k}} \right)$$ and $$\left( {0,0,{{3\pi } \over k}} \right)$$, respectively, have the same velocity of 0.5 c $$\widehat i$$, (where c is the velocity of light). The ratio of the force acting on charge q₁ to q₂ is :-

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20cos(2 $$\times$$ 10¹⁰ t $$-$$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $$\mu$$_r = 1)

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm^$$-$$1. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :