Assignment Set-2

For an electromagnetic wave described by $B=8\times {10}^{-6}\sin \left(5000\pi x-3\times {10}^{11}\mathrm{\pi }t\right)$, where $B$ is in tesla, $x$ is in metre and $t$ is in second. If speed of wave is $N\times {10}^7 \mathrm{m} {\mathrm{s}}^{-1}$, then value of $N$ is _____ .

The electric field of a plane electromagnetic wave is given by $E=E_0\sin (kz-\omega t)[\hat{\mathrm{i}}+\hat{\mathrm{j}}]$. If direction of the associated magnetic field is $a\hat{\mathrm{i}}+b\hat{\mathrm{j}}$, then value of $(a+b)$ is _____ .

In EM waves, the phase difference between electric field and magnetic field vectors is _____ .

A parallel plate capacitor consists of two circular plates of area $100{ \mathrm{cm}}^2$ each. The separation between the plates is $1 \mathrm{mm}$. If the displacement current is $17.7 \mathrm{A}$, then the rate of change of electric field between the plates is $2\times {10}^N \mathrm{N} {\mathrm{C}}^{-1}{ \mathrm{s}}^{-1}$, the value of $N$ is _____ .

(Take ${\epsilon }_0=8.85\times {10}^{-12} \mathrm{F} {\mathrm{m}}^{-1}$)

The electric field between the plates of a parallel plate capacitor having plate area $4{ \mathrm{cm}}^2$ is changing at the rate of $3\times {10}^{12 }\mathrm{N} {\mathrm{C}}^{-1}{ \mathrm{s}}^{-1}$. The displacement current is _____ $\mathrm{mA}$.

Give an answer to the nearest integer value.

An electromagnetic wave propagating through vacuum is given by $B=2.0\times {10}^{-6}\sin (kx-3.0\times {10}^{6}t) \mathrm{T}$  where $x$ is in metre and $t$ is in second. The value of $k$ is _____ ${\mathrm{m}}^{-1}$.

The dimensional formula of $\frac{{\mu }_{0}d{\varphi }_E}{dt}$ where ${\varphi }_E$ represents electric flux and $t$ represents time, is $\left[{\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}\mathrm{T}{}^{\mathrm{c}}\mathrm{I}^{\mathrm{d}}\right]$. Find $\left|\right(a+b+c+d\left)\right|$.

The amplitude of magnetic field at a distance $r$ from a point source of power $P$ (considering $100\%$ efficiency) is $\sqrt{\frac{{\mu }_{0}P}{k\pi r^{2}C}}$, the value of $k$ is _____ .