The electric field of an electromagnetic wave in free space is given by $\vec E$$=10 cos (10^7t+kx)$$\hat j$ $volt/m $ where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
$(1)$ the wavelength $\lambda$ is $188.4\, m.$
$(2)$ the wave number $k$ is $0.33\,\, rad/m.$
$(3)$ the wave amplitude is $10\, V/m.$
$(4)$ the wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct ?
The electric field of an electromagnetic wave in free space is given by $\vec E$$=10 cos (10^7t+kx)$$\hat j$ $volt/m $ where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
$(1)$ the wavelength $\lambda$ is $188.4\, m.$
$(2)$ the wave number $k$ is $0.33\,\, rad/m.$
$(3)$ the wave amplitude is $10\, V/m.$
$(4)$ the wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct ?
- [AIPMT 2010]
- A
$(3)$ and $(4)$
- B
$(1)$ and $(2)$
- C
$(2)$ and $(3)$
- D
$(1)$ and $(3)$
Similar Questions
The electromagnetic waves travel in a medium at a speed of $2.0 \times 10^{8}\, m / s$. The relative permeability of the medium is $1.0.$ The relative permittivity of the medium will be
The electromagnetic waves travel in a medium at a speed of $2.0 \times 10^{8}\, m / s$. The relative permeability of the medium is $1.0.$ The relative permittivity of the medium will be
- [JEE MAIN 2022]
In the $EM$ wave the amplitude of magnetic field $H_0$ and the amplitude of electric field $E_o$ at any place are related as
In the $EM$ wave the amplitude of magnetic field $H_0$ and the amplitude of electric field $E_o$ at any place are related as
The optical properties of a medium are governed by the relative permitivity $({ \in _r})$ and relative permeability $(\mu _r)$. The refractive index is defined as $n = \sqrt {{ \in _r}{\mu _r}} $. For ordinary material ${ \in _r} > 0$ and $\mu _r> 0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist V. Veselago postulated the existence of material with $\in _r < 0$ and $u_r < 0$. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $n = - \sqrt {{ \in _r}{\mu _r}} $. As light enters a medium of such refractive index the phases travel away from the direction of propagation.
$(i) $ According to the description above show that if rays of light enter such a medium from air (refractive index $=1)$ at an angle $\theta $ in $2^{nd}$ quadrant, then the refracted beam is in the $3^{rd}$ quadrant.
$(ii)$ Prove that Snell's law holds for such a medium.
The optical properties of a medium are governed by the relative permitivity $({ \in _r})$ and relative permeability $(\mu _r)$. The refractive index is defined as $n = \sqrt {{ \in _r}{\mu _r}} $. For ordinary material ${ \in _r} > 0$ and $\mu _r> 0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist V. Veselago postulated the existence of material with $\in _r < 0$ and $u_r < 0$. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $n = - \sqrt {{ \in _r}{\mu _r}} $. As light enters a medium of such refractive index the phases travel away from the direction of propagation.
$(i) $ According to the description above show that if rays of light enter such a medium from air (refractive index $=1)$ at an angle $\theta $ in $2^{nd}$ quadrant, then the refracted beam is in the $3^{rd}$ quadrant.
$(ii)$ Prove that Snell's law holds for such a medium.
A monochromatic beam of light has a frequency $v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz$ and is propagating along the direction $\frac{{\hat i + \hat j}}{{\sqrt 2 }}$. It is polarized along the $\hat k$ direction. The acceptable form for the magnetic field is
A monochromatic beam of light has a frequency $v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz$ and is propagating along the direction $\frac{{\hat i + \hat j}}{{\sqrt 2 }}$. It is polarized along the $\hat k$ direction. The acceptable form for the magnetic field is
- [JEE MAIN 2018]
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
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