Electric Field vs Magnetic Field

Q.

The magnetic potential energy stored in a certain inductor is 25 $mJ$, when the current in the inductor is 60 $mA$. The inductor is of inductance

1. 0.138 $H$
2. 1.389 $H$
3. 138.88 $H$
4. 13.89 $H$

Q. A) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels.

B) Using the Bohr’s model calculate the orbital period in the 𝑛 = 1, 2, and 3 levels. (Speed of electron in 𝑛=1, 2 and 3 level is $2.18\times {10}^{6}m/s;1.09\times {10}^{6}m/s;7.27\times {10}^{5}m/s$ respectively)
$=6.6\times {10}^{-34}Js$
$T_3=\frac{1}{(7.27\times {10}^5)}$
$\left(\frac{\left(3{)}^2\right(6.6\times {10}^{-34}{)}^2}{2\times 3.14(9.1\times {10}^{-31})(9\times {10}^9)(1.6\times {10}^{-19}{)}^2}\right)$
$T-3=4.11\times {10}^{-15}s$
Final answer : $1.52\times {10}^{-16}s;$
$1.22\times {10}^{-15}s;4.11\times {10}^{-15}s$

Q. Ratio of average electric field $\left(E\right)$ to average magnetic field ($B$) is

1. speed of light
2. speed of oscillating particle
3. electric field of $EM$ wave
4. magnetic field of $EM$ wave

Q.

To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog, the intensity $\left(\frac{power}{area}\right)S$ of the light from the signal, and its frequency $f$. The engineer finds that $d$ is proportional to $S^{\frac{1}{n}}$. The value of $n$

1. $2$

2. $3$

3. $1$

4. $4$

Q.

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{Wm}}^{-2}$falls normally on a polarizer (cross sectional area $3\times {10}^{-4}{\mathrm{m}}^2$) which rotates about its axis with an angular speed of $31.4\mathrm{rad}/\mathrm{s}$. The energy of light passing through the polarizer per revolution is close to:

1. $1.0\times {10}^{-4}\mathrm{J}$

2. $1.0\times {10}^{-5}\mathrm{J}$

3. $5.0\times {10}^{-4}\mathrm{J}$

4. $1.5\times {10}^{-4}\mathrm{J}$

Q.

The electric field of a plane electromagnetic wave propagating along the x-direction in a vacuum is $\overrightarrow{E}=E_{\circ }\hat{j}\cos \left(\omega t-kx\right)$.The magnetic field $\overrightarrow{B}$ at the moment $t=0$ is:

1. $\overrightarrow{B}=\frac{E_{\circ }}{\sqrt{{\mu }_{\circ }{\epsilon }_{\circ }}}\cos \left(kx\right)\hat{j}$

2. $\overrightarrow{B}=\frac{E_{\circ }}{\sqrt{{\mu }_{\circ }{\epsilon }_{\circ }}}\cos \left(kx\right)\hat{k}$

3. $\overrightarrow{B}=E_{\circ }\sqrt{{\mu }_{\circ }{\epsilon }_{\circ }}\cos \left(kx\right)\hat{j}$

4. $\overrightarrow{B}=E_{\circ }\sqrt{{\mu }_{\circ }{\epsilon }_{\circ }}\cos \left(kx\right)\hat{k}$

Q. An electron (mass = $9.1\times {10}^{-31}\text{kg}$ charge $=-1.6\times {10}^{-19}\text{C}$) experiences no deflection if subjected to an electric field of $3.2\times {10}^5\text{V/m}$ and a magnetic field of $2.0\times {10}^{-3}{\text{Wb/m}}^2$. Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit of radius

1. $45\text{m}$
   
2. $4.5\text{m}$
3. $0.45\text{m}$
4. $0.045\text{m}$
   

Q.

If $\overrightarrow{E}$ and $\overrightarrow{B}$ are the electric and magnetic field vectors of E.M. waves then the direction of propagation of E.M. wave is along the direction of

1. $\overrightarrow{E}$

2. $\overrightarrow{B}$

3. $\overrightarrow{E}\times \overrightarrow{B}$

4. None of these

Q. The electric and the magnetic field, associated with an $EM$ wave, propagating along the $+z$-axis, can be represented by

1. $\overrightarrow{E}=E_0\hat{j},\overrightarrow{B}=B_0\hat{k}$
2. $\overrightarrow{E}=E_0\hat{i},\overrightarrow{B}=B_0\hat{j}$
3. $\overrightarrow{E}=E_0\hat{k},\overrightarrow{B}=B_{\circ }\hat{i}$
4. $\overrightarrow{E}=E_0\hat{j},\overrightarrow{B}=B_0\hat{i}$

Q. A light beam travelling in the X-direction is described by the electric field $E_y=\left(300\text{V/m}\right)\sin \omega (t-x/c).$ An electron is constrained to move along the Y-direction with a speed of $2.0\times {10}^7\text{m/s}.$ Find the maximum electric force and the maximum magnetic force on the electron respectively.

1. $3.6\times {10}^{-17}\text{N},2.5\times {10}^{-18}\text{N}$
2. $4.8\times {10}^{-17}\text{N},3.2\times {10}^{-18}\text{N}$
3. $9.6\times {10}^{-17}\text{N},6.4\times {10}^{-18}\text{N}$
4. $2.4\times {10}^{-17}\text{N},1.6\times {10}^{-18}\text{N}$

Q. A proton has spin and magnetic moment just like an electron. Why then its effect is neglected in magnetism of materials?

Q.

$1)$ In $1959$ Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be:

$e_p=–(1+y)e$

where e is the electronic charge.

$A)$ Find the critical value of $y$ such that expansion may start.

$2)$ In $1959$ Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be:

$e_p=–(1+y)e$

where e is the electronic charge.

$B)$ Show that the velocity of expansion is proportional to the distance from the centre.

Q. A light beam travelling in the x-direction is described by the electric field $E_y=300V{m}^{-1}sin\omega (t-\frac{x}{c})$. An electron is constrained to move along the y-direction with a speed of $2.0\times {10}^{7}m{s}^{-1}$. Find the maximum electric force and the maximum magnetic force on the electron.

1. $F_E=4.8\times {10}^{-17}N$ and $F_B=3.2\times {10}^{-18}N$
2. $F_E=8.4\times {10}^{-18}N$ and $F_B=3.2\times {10}^{-18}N$
3. $F_E=3.2\times {10}^{-17}N$ and $F_B=4.8\times {10}^{-18}N$
4. $F_E=4.8\times {10}^{-17}N$ and $F_B=6.4\times {10}^{-17}N$

Q. A bar magnet of magnetic moment $2{\text{Am}}^2$ is free to rotate about a vertical axis passing through its centre. The magnet is then released from rest at east -west position. Find the Kinetic energy of the magnet as it takes north-south position is ________$\mu \text{J}$ $(B_H=25\mu \text{T})$ (Give integer value)

Q. Amplitude of electric field in a laser beam of power 4.4 mW with cross-sectional area of $2m{m}^2$ is

1. $2kV/m$
2. $\frac{23}{2}kV/m$
3. $\sqrt{\frac{2}{3}}kV/m$
4. $\sqrt{\frac{5}{3}}kV/m$

Q.

The intensity of the sunlight reaching the earth is $1.380W{m}^{-2}$ Assume this light to be a plane, monochromatic wave. Find the amplitudes of electric and magnetic fields in this wave

Q. The approximate operating magnetic field for accelerating protons in a cyclotron oscillator having frequency of $12\text{MHz}$ is:

1. $0.790\text{T}$
2. $0.690\text{T}$
3. $0.395\text{T}$
4. $0.345\text{T}$

Q. A proton beam passes without deviation through the region of space where there exists uniform transverse mutually perpendicular electric and magnetic field with $E=120\text{kV/m}$ and $B=50\text{mT}$. The beam strikes a ground target. Find the force imparted by the beam on the target if the beam current is equal to $0.80\text{mA}$.

1. $15.4\mu \text{N}$
2. $19.2\mu \text{N}$
3. $28.2\mu \text{N}$
4. $45\mu \text{N}$

Q. A non-relativistic proton beam passes without deviation through the region of space where uniform transverse mutually perpendicular electric and magnetic fields of $E=120{\text{kVm}}^{-1}$ and $B=50\text{mT}$. Then the beam strikes a grounded target. Find the force with which the beam hits on the target if the beam current is equal to $I=0.80\text{mA}$.[Take mass of proton and its charge as $m_e=1.67\times {10}^{-27}\text{kg}$ and $q=1.6\times {10}^{-19}\text{C}$ respectively.]

1. $10\mu \text{N}$
2. $40\mu \text{N}$
3. $30\mu \text{N}$
4. $20\mu \text{N}$

Q.

A laser beam has intensity $2.5\times {10}^{14}$ W $m^{-2}$ Find the amplitudes of electric and magnetic fields in the beam.

Q. Maximum value of electric field at a point at a distance of 2 m from the light source of power 60 watt is

1. $50N/C$
2. $30N/C$
3. $2\times {10}^{-3}N/C$
4. $5\times {10}^{-3}N/C$

Q. At the threshold of detection, an FM receiver can pick up a signal for which $E_0=2\mu \text{V/m}$. The intensity of the electromagnetic wave is -

1. $5.31\times {10}^{-15}{\text{W-m}}^{-2}$
2. $5.31\times {10}^{-12}{\text{W-m}}^{-2}$
3. $5.31\times {10}^{-14}{\text{W-m}}^{-2}$
4. $5.31\times {10}^{-17}{\text{W-m}}^{-2}$

Q. Write the relation for the speed of electromagnetic waves and the amplitudes of electric and magnetic fields.

Q. (a) Give three reasons why modulation of a message signal is necessary for long distance transmission.
(b) Show graphically an audio signal, a carrier wave and an amplitude modulated wave

Q. The electric field associated with a light wave is given by $E=E_0\sin \left[\right(1.57\times {10}^7\left)\right(x-ct\left)\right]$(where, x and t are in metre and second). The stopping potential when its light is used in an experiment on photoelectric effect with the emitter having work function $\varphi =19$eV is?

1. $1.8$eV
2. $0.6$eV
3. $2.4$eV
4. $1.2$eV

Q. The sunlight reaching the earth has maximum electric field of $810V/m$. What is the maximum magnetic field in this light?

1. $2.7\mu T$
2. $1.8\mu T$
3. $0.9\mu T$
4. $0.3\mu T$

Q. The short-wavelength limit shifts by $26\text{pm}$ when the operating voltage in an X-ray tube is increased to $1.5$ times the original value. What was the original value of the operating voltage?

1. $25.56\text{kV}$
2. $36.78\text{kV}$
3. $15.93\text{kV}$
4. $8.12\text{kV}$

Q. A light beam travelling in the $x-$ direction is described by the electric field $E_y=\left(300{\text{Vm}}^{-1}\right)\sin \omega (t-x/c)$. An electron is constrained to move along the $y-$direction with a speed of $2.0\times {10}^7{\text{ms}}^{-1}$. If the maximum electric force acting on the electron is $F_E$ and the maximum magnetic force acting on the electron is $F_B$, then

1. $F_E=1.60\times {10}^{-17}\text{N}$
2. $F_E=4.8\times {10}^{-17}\text{N}$
3. $F_B=1.6\times {10}^{-18}\text{N}$
4. $F_E>F_B$

Q. In a plane electromagnetic wave, the electric field of amplitude $1V{m}^{-1}$ varies with time in free space. The average energy density of magnetic field is (in $J{m}^{-2}$)

1. $8.86\times {10}^{-12}$
2. $17.72\times {10}^{-12}$
3. $4.43\times {10}^{-12}$
4. $1.11\times {10}^{-12}$
5. $2.21\times {10}^{-12}$

Q. In a wave $E_0=100{Vm}^{-1}$. Find the Poynting vector magnitude.

1. $13.25{Wm}^{-2}$
2. $26.5{Wm}^{-2}$
3. $18.25{Wm}^{-2}$
4. $19.7{Wm}^{-2}$