The quantities $x = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$,$y = \frac{E}{B}$,and $z = \frac{l}{CR}$ are defined,where $C$ is capacitance,$R$ is resistance,$l$ is length,$E$ is electric field,$B$ is magnetic field,and $\varepsilon_{0}, \mu_{0}$ are free space permittivity and permeability respectively. Then:
- AOnly $x$ and $y$ have the same dimension
- B$x, y$ and $z$ have the same dimension
- COnly $x$ and $z$ have the same dimension
- DOnly $y$ and $z$ have the same dimension
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Similar Questions
If a source is transmitting electromagnetic waves of frequency $8.2 \times 10^6 \ Hz$,then the wavelength of the electromagnetic waves transmitted from the source will be.....$m$.
Easy
View SolutionAn electromagnetic wave of frequency $1 \times 10^{14} \,Hz$ is propagating along the $z$-axis. The amplitude of the electric field is $4 \,Vm^{-1}$. What is the energy density of the electric field? (Permittivity of free space $\varepsilon_0 = 8.8 \times 10^{-12} \,C^2 \,N^{-1} \,m^{-2}$)
In a plane electromagnetic wave,the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10} \; Hz$ and amplitude $48 \; V m^{-1}$.
$(a)$ What is the wavelength of the wave?
$(b)$ What is the amplitude of the oscillating magnetic field?
$(c)$ Show that the average energy density of the $E$ field equals the average energy density of the $B$ field. $[c = 3 \times 10^{8} \; m s^{-1}]$.
$(a)$ What is the wavelength of the wave?
$(b)$ What is the amplitude of the oscillating magnetic field?
$(c)$ Show that the average energy density of the $E$ field equals the average energy density of the $B$ field. $[c = 3 \times 10^{8} \; m s^{-1}]$.
Medium
View Solution$A$ plane electromagnetic wave is travelling in the positive $X$-axis. At the instant shown,the electric field at the extremely narrow dashed rectangle is in the $-ve$ $Z$-direction and its magnitude is increasing. Which diagram correctly shows the direction and relative magnitudes of the magnetic field at the edges of the rectangle?
Medium
View SolutionIf an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$,then the velocity of light is greater in vacuum than that in this medium by . . . . . . times. $\left(\mu_0=4 \pi \times 10^{-7} \ H/m, \varepsilon_0=8.85 \times 10^{-12} \ F/m, c=3 \times 10^8 \ m/s\right)$
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