Physics

This is a short answer type question as classified in NCERT Exemplar

Magnetic field induction at a point in a region between two plates of a parallel plate capacitor is

B= $\frac{{\mu }_{0}2I_d}{4\pi r}$ = $\frac{{\mu }_0{I}_d}{2\pi r}$ = $\frac{{\mu }_0}{2\pi r}?$ 0 $\frac{d{\varnothing }_E}{dt}$

= $\frac{{\mu }_{0{?}_0}}{2\pi r}\frac{d}{dt}$  (E $\pi r^2$ ) = $\frac{{\mu }_{0{?}_0}}{2\pi r}\pi r^2\frac{d}{dt}$  (E)

B= $\frac{{\mu }_{0{?}_{0r}}}{2\pi r}\frac{d}{dt}$  (E)

This is a short answer type question as classified in NCERT Exemplar

An electromagnetic wave carries energy and momentum like other waves.

Since, it carries momentum, an electromagnetic wave also exerts pressure called radiation pressure. This property of electromagnetic waves helped professor CV Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. The tails of the camets are also due to radiation pressure.

This is a short answer type question as classified in NCERT Exemplar

Consider and electromagnetic waves, let E be varying along y-axis, B is along z-axis and propagation of wave be along x-axis. Then E*B will tell the direction of propagation of

energy flow in electromagnetic wave, along x-axis.

E= E₀sin (wt-kx)j

B=B₀sin (wt=kx)k

So S will become $\frac{E_0{B}_0}{{\mu }_0}$ sin² (wt-kx)i

And its variation with time is given below

This is a short answer type question as classified in NCERT Exemplar

Aaverage magnetic energy density I_av= $\frac{1}{2}\frac{B^2}{{\mu }_0}$ c

From eqn we know that B=12 $*{10}^{-8}$

= $\frac{1}{2}*\frac{({12*{10}^{-8})}^2*3*{10}^8}{4\pi *{10}^{-7}}$ = 1.71W/m²

This is a short answer type question as classified in NCERT Exemplar

X_c=1/2 $\pi fc$

And displacement current is inversely proportional to X_c so when capacitive reactance increases then displacement current will decrease.

This is a short answer type question as classified in NCERT Exemplar

I_d=I_c= dq/dt

And q=q₀ cos 2πvt

By putting this in above equation I_d=I_c= q₀ sin2πvt $*$ 2 $\pi \upsilon$

This is a short answer type question as classified in NCERT Exemplar

Microwave oven heats up the food items containing water molecules most efficiently because the frequency of microwaves matches the resonant frequency of water molecules.

This is a short answer type question as classified in NCERT Exemplar

The orientation of the portable radio with respect to broadcasting station is important because the electromagnetic waves are plane polarised, so the receiving antenna should be parallel to the vibration of the electric or magnetic field of the wave.

This is a long answer type question as classified in NCERT Exemplar

(i) U_E= $\frac{1}{2}{\epsilon }_o{E}^2$

U_B= $\frac{1}{2}\frac{B^2}{{\mu }_o}$

So total energy density = U_E+ U_B= $\frac{1}{2}{\epsilon }_o{E}^2$ + $\frac{1}{2}\frac{B^2}{{\mu }_o}$

E= Eo/ $\sqrt[]{2}$  and B=Bo/ $\sqrt[]{2}$

U_av= $\frac{1}{4}{\epsilon }_o{E}^2$ + $\frac{1}{4}\frac{B^2}{{\mu }_o}$

(ii) We know Eo=cBo and c = 1/ $\sqrt[]{{\mu }_0{\epsilon }_0}$

$\frac{1}{4}\frac{B^2}{{\mu }_o}=\frac{1}{4}\frac{\frac{{Eo}^2}{c^2}}{{\mu }_o}$ = 1/4 $\epsilon oEo$ ²

U_E= U_B

This is a long answer type question as classified in NCERT Exemplar

(i) $\left(i\right)\int E.dl$ = ${\int }_1^{2}E.dl+{\int }_2^{3}E.dl+{\int }_3^{4}E.dl+{\int }_4^{1}E.dl$

= E_oh[sin(kz₂-wt)-sin(kz₁-gwt)]

(ii) $\int B.ds=\int B.dscos0={\int }_{z1}^{z2}{B}_0\mathrm{s}\mathrm{i}\mathrm{n}?(kz-wt)hdz$

= $\frac{-B_{o}h}{k}\cos ?\left(kz2-wt\right)\cos ?\left(kz1-wt\right)$

(iv) $?E.dl=\frac{-d\varnothing }{dt}$ =- $?B.ds$

=Eoh[sin(kz2-wt)-sin(kz1-wt)]

=- $\frac{d}{dt}[\frac{B_{yh}}{k}\cos ?\left(kz2-wt\right)-\mathrm{c}\mathrm{o}\mathrm{s}?(kz1-wt\left)\right]$

Eo=Bow/k=Byc

Eo/Bo=c