The magnetic field in the plane electromagnetic wave is given by

$B_z=2\times {10}^{-7}\sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t) tesla$

The expression for the electric field will be

(1) $E_z=30\sqrt{2} \sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t) V/m$

(2) $E_z=60 \sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t) V/m$

(3) $E_y=30\sqrt{2} \sin (0.5\times {10}^{11}x+1.5\times {10}^{3}t) V/m$

(4) $E_y=60 \sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t) V/m$

 

In an electromagnetic wave, if the electric field oscillated sinusoidally with an amplitude of \(48~\text{Vm}^{-1}\), then the RMS value of the oscillating magnetic field will be:
1. \(1.6\times 10^{-8}~\text{T}\)
2. \(1.6\times 10^{-9}~\text{T}\)
3. \(144\times 10^{-8}~\text{T}\)
4. \(11.3\times 10^{-8}~\text{T}\)

A plane electromagnetic wave propagating in the x-direction has wavelength of 60 mm. The electric field is in the y-direction and its maximum magnitude is 33 V/$m^{-1}$. The equation for the electric field as function of x and t is

(1) 11 sin $\mathrm{\pi }$(t - x/c)

(2) 33 sin $\mathrm{\pi }\times {10}^{10}$ (t - x/c)

(3) 33 sin $\mathrm{\pi }$(t - x/c)

(4) 11 sin $\mathrm{\pi }\times {10}^{11}$(t - x/c)

In a region of free space, the electric field at some instant of time is $\overrightarrow{E}=(80\hat{i}+32\hat{j}-64\hat{k})$V/m and the magnetic field is $\overrightarrow{B}=(0.2\overrightarrow{i}+0.08\hat{j}+0.29\hat{k})\mu T$. The Poynting vector for these fields is

(1) $-11.52\hat{i}+28.8\hat{j}$

(2) $-28.8\hat{i}+11.52\hat{i}$

(3) $28.8\hat{i}-11.52\hat{j}$

(4) $11.52\hat{i}-28.8\hat{j}$

The sun delivers \(10^{3}~\text{W/m}^2\) of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions \(8\) m$\times$\(20\) m will be:
1. \(2.56\times 10^{4}~\text{W}\)
2. \(6.4\times 10^{5}~\text{W}\)
3. \(4.0\times 10^{5}~\text{W}\)
4. \(1.6\times 10^{5}~\text{W}\)

A parallel plate capacitor with plate area \(A\) and separation between the plates \(d\), is charged by a source having current \(i\) at some instant. Consider a plane surface of area \(A/2\) parallel to the plates and drawn symmetrically between the plates. The displacement current through this area is:
1. \(i\) 
2. \(i/2\) 
3. \(i/4\) 
4. \(i/8\)

A larger parallel plate capacitor, whose plates have an area of \(1~\text{m}^2,\) separated from each other by \(1\) mm, is being charged at a rate of \(25.8\) V/s. If the plates have dielectric constant \(10\), then the displacement current at this instant is:
1. \(25~\mu\text{A}\)
2. \(11~\mu\text{A}\)
3. \(2.2~\mu\text{A}\)
4. \(1.1~\mu\text{A}\)

The magnetic field between the plates of radius 12 cm separated by a distance of 4 mm of a parallel plate capacitor of capacitance 100 pF along the axis of plates having conduction current of 0.15 A is

(1) zero

(2) 1.5 T

(3) 15 T

(4) 0.15 T

A plane electromagnetic wave

$E_z=100 \cos (6\times {10}^{8}t+4x) V/m$

propagates in a medium of dielectric constant

(1) 1.5

(2) 2.0

(3) 2.4

(4) 4.0

The energy of the X-rays photon is 3.3$\times {10}^{-16}$J. Its frequency is :

(1) $2\times {10}^{19} Hz$

(2) $5\times {10}^{18} Hz$

(3) $5\times {10}^{17} Hz$

(4) $5\times {10}^{16} Hz$