Maxwell's Equations

Q.

State the Gauss law of magnetism.

Q.

A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor is of same capacity is connected in parallel with it. Then energy stored in each capacitor is

1. $\frac{U}{2}$

2. $\frac{U}{4}$

3. $4U$

4. $2U$

Q.

What is the SI unit of intensity?

Q.

An α-particle moves in a circular path of radius $0.83cm$ in the presence of a magnetic field of $0.25Wb/m^2$. The de Broglie wavelength associated with the particle will be:

1. $1\dot{A}$

2. $0.1\dot{A}$

3. $10\dot{A}$

4. $0.01\dot{A}$

Q. Two parallel metal plates having charge $+Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

1. Become zero
2. Increase
3. Decrease
4. Remain same

Q.

A signal of $0.1kW$ is transmitted in a cable. The attenuation of cable is $-5dBperkm$ and cable length is$20km$. The power received at receiver is ${10}^{-x}W$. The value of $x$ is ______.

Q.

An electromagnetic wave of frequency $3GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be _______ $\times {10}^{-2}cm$.

Q.

What does the area under the Maxwell distribution curve represent?

Q.

Why the capacitor is connected in parallel?

Q. A source of light is placed in front of a screen. Intensity of light on the screen is $I$. Two Polaroids $P_{1}and{P}_2$ are so placed in between the source of light and screen that the intensity of light on screen is $\frac{I}{2}$. $P_2$ should be rotated by an angle of ____(degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

Q. Consider the situation shown in figure. If the switch is closed and after some time it is opened again, the closed loop will show

1. an anticlockwise current-pulse.
2. a clockwise current-pulse.
3. an anticlockwise current-pulse and then a clockwise current -pulse
4. a clockwise current-pulse and then an anticlockwise current -pulse.

Q. A cyclotron in which protons are accelerated has a flux density of $1.57\text{T}$. The frequency of variation of electric field is

1. $4.8\times {10}^6\text{Hz}$
2. $4.8\times {10}^8\text{Hz}$
3. $8.4\times {10}^8\text{Hz}$
4. $2.4\times {10}^7\text{Hz}$

Q. A parallel plate capacitor having a separation between the plates $d$ , plate area $A$ and material with dielectric constant $k$ has capacitance $C_o$ . Now one third of the material is replaced by another material with dielectric constant $2k$, so that effectively there are two capacitors one with area $\frac{A}{3}$, dielectric constant $2k$ and another with area $\frac{2A}{3}$ and dielectric constant $k$. If the capacitance of this new capacitor is $C$ then the value of $\frac{C}{C_0}$ is:

1. $1$
2. $\frac{4}{3}$
3. $\frac{1}{3}$
4. $\frac{2}{3}$

Q. Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is n = 50.0 MHz. (a) Determine, B0, w, k, and l. (b) Find expressions for E and B.

Q. A variable air capacitor in a tuning circuit is made up of $N$ semicircular plates, each of radius $R$ and positioned at a distance $d$ from its neighbours, to which it is electrically connected as shown in figure, a second identical set of plates is enmeshed with its plates halfway between those of the first set. The second set can rotate as a unit. Determine the capacitance as a function of the angle of rotation $\theta$, where $\theta =0^{\circ }$ corresponds to the maximum capacitance.

1. $\frac{2N\sin \theta \pi R^2{\epsilon }_0}{d}$
2. $\frac{(2N-1)\sin \theta \pi R^2{\epsilon }_0}{d}$
3. $\frac{2N(\pi -\theta )R^2{\epsilon }_0}{d}$
4. $\frac{(2N-1)(\pi -\theta )R^2{\epsilon }_0}{d}$

Q. The figure shows a network of currents. The current $i$ will be

1. $3\text{A}$
2. $13\text{A}$
3. $23\text{A}$
4. $-3\text{A}$

Q.

A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density $6g{m}^{-1}$ kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2.0 m long portion of the string.

Q.

Unification of electricity magnetism and optics was given by

Q.

The displacement current flows in the dielectric of a capacitor when the potential difference across its plates__________

Q. The wavelength of $K_{\alpha }\text{X-ray}$ of tungsten is $21.3\text{pm}$. It takes $11.3\text{keV}$ to knock out an electron from the $\text{L-shell}$ of a tungsten atom. What should be the minimum accelerating voltage across an X-ray tube having a tungsten target which allows production of $K_{\alpha }\text{X-ray}$? $(hc=1242\text{eV-nm})$

1. $53.8\text{kV}$
2. $74.5\text{kV}$
3. $89.2\text{kV}$
4. $69.6\text{kV}$

Q. The separation between the plates of a pre-charged parallel plate capacitor is increased. Which of the following quantities will change?

1. Charge on the capacitor
2. Potential difference across the capacitor
3. Energy of the capacitor
4. Energy density between the plates of the capacitor.

Q. In which directions do the electric and magnetic field vectors oscillate in an electromagnetic wave propogating along the X-axis ?

Q. Write the mathematical equation of 'Ampere-Maxwell law'.

Q. A plane electromagnetic wave propagating in the $x-$direction in vacuum has wavelength of $6.0\text{mm}$. The electric field is in the $y-$direction and its maximum magnitude is $33{\text{Vm}}^{-1}$.

$\left(ii\right)$ The equation for the magnetic field as a function of $x\left(\text{m}\right)$ and $t\left(\text{s}\right)$ is

​​​​​​​$[$1 Mark$]$

1. $\overrightarrow{B}=11\times {10}^{-8}\sin \left[\pi (t-\frac{x}{c})\right]\hat{i}$
2. $\overrightarrow{B}=11\times {10}^{-8}\sin [\pi \times {10}^{11}(t-\frac{x}{c})]\hat{i}$
3. $\overrightarrow{B}=11\times {10}^{-8}\sin [\pi \times {10}^{11}(t-\frac{x}{c})]\hat{j}$
4. $\overrightarrow{B}=11\times {10}^{-8}\sin [\pi \times {10}^{11}(t-\frac{x}{c})]\hat{k}$

Q.

The magnetic field due to current element depends upon which of the following factors:

1. Current flowing through it.

2. Distance from it.

3. Its length.

4. All of above.

Q. The displacement current of $4.425\mu A$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of ${10}^{6}V{s}^{–1}$. The area of each plate of the capacitor is $40c{m}^2$. The distance between each plate of the capacitor is $x\times {10}^{–3}m$. The value of $x$ is,
(Permittivity of free space, $\varepsilon_0 = 8.85 \times 10^{–12} C^2 N^{–1} m^{–2}) \)

Q.

What are electromagnetic waves? Give examples.

Q. What are electromagnetic waves? Describe Maxwell's electromagnetic theory in brief.

Q. Which of the following is true in case of a dielectric strength, when the thickness of the material increases?

1. Increases
2. Remains same
3. Decreases
4. Becomes zero

Q. A and B are two concentric hollow spheres. If A is given a charge Q while B is earthed as shown in figure.

1. The charge density of A and B are same
2. The field inside and outside A is zero
3. The field between A and B is not zero
4. The field inside and outside B is zero