The magnetic field in a plane electromagnetic wave is given by, $B_{y}=2 \times 10^{-7} \sin \left(\pi \times 10^{3} x+3 \pi \times 10^{11} t\right) \;T$ Calculate the wavelength.

A plane electromagnetic wave with frequency of $30 {MHz}$ travels in free space. At particular point in space and time, electric field is $6 {V} / {m}$. The magnetic field at this point will be ${x} \times 10^{-8} {T}$. The value of ${x}$ is ..... .

An electron is constrained to move along the $y-$axis with a speed of $0.1\, c$ (c is the speed of light) in the presence of electromagnetic wave, whose electric field is $\overrightarrow{ E }=30 \hat{ j } \sin \left(1.5 \times 10^{7} t -5 \times 10^{-2} x \right)\, V / m$ The maximum magnetic force experienced by the electron will be: (given $c=3 \times 10^{8}\, ms ^{-1}$ and electron charge $\left.=1.6 \times 10^{-19} C \right)$

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

The monoenergetic beam of electrons moving along $+ y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected, then fields $B$ and $E$ are directed respectively along

An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+ y$ direction . Its magnetic field is along $+\, x-$ axis. The vector equation for the associated electric field ( of amplitude $E_0$) is