Displacement Current

Q. A $100\Omega$ resistance and a capacitor of $100\Omega$ reactance are connected in series across a $220V$ source. When the capacitor is $50\%$ charged, the peak value of the displacement current is

1. $4.4A$
2. $11\sqrt{2}A$
3. $2.2A$
4. $11A$

Q. Two charges $+5\mu \text{C}$ and $+10\mu \text{C}$ are placed $20\text{cm}$ apart. The electric field at the mid-point between the two charges will be:

1. $12.5\times {10}^6\text{N/C}\text{towards}+10\mu \text{C}$
2. $12.5\times {10}^6\text{N/C}\text{towards}+5\mu \text{C}$
3. $4.5\times {10}^6\text{N/C}\text{towards}+10\mu \text{C}$
4. $4.5\times {10}^6\text{N/C}\text{towards}+5\mu \text{C}$

Q. A uniform electric field $E$ is created between two parallel and oppositely charged plates as shown in figure. An electron enters the field symmetrically between the plates with a speed $v_0$. The length of each plate is $l$. Find the angle of deviation (which is given by $\theta$ in the figure) of the path of the electron as it comes out of the field interms of mass of electron $m$ and charge of the electron $e$. (Acceleration due to gravity can be neglected)

1. $\theta ={\tan }^{-1}\left(\frac{2eEl}{m{v}_0^2}\right)$
2. $\theta ={\tan }^{-1}\left(\frac{eEl}{m{v}_0^2}\right)$
3. $\theta ={\cot }^{-1}\left(\frac{2eEl}{m{v}_0^2}\right)$
4. $\theta ={\tan }^{-1}\left(\frac{eE}{m{v}_0^2}\right)$

Q. (a) Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density $\sigma$ (b) An infinitely large thin plane sheet has a uniform surface charge density $+\sigma$ . Obtain the expression for the amount of work done in bringing a point charge q from infinity. to a point, distant r, in front of the charged plane sheet.

Q.

What was the electromagnetic theory of Max­well?

Q. In an electromagnetic wave in free space, the root mean square value of the electric field is $E_{rms}=6V{m}^{-1}$. The peak value of the magnetic field is

1. $2.83\times {10}^{-8}T$
2. $0.70\times {10}^{-8}T$
3. $4.23\times {10}^{-8}T$
4. $1.41\times {10}^{-8}T$

Q. A parallel-plate capacitor with plate area A and separation between the plates d is charged by a constant current i. Consider a plane surface of area $\frac{A}{2}$ parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

1. $\frac{i}{5}$
2. $\frac{i}{2}$
3. $i$
4. $\frac{i}{3}$

Q. A slab of material of dielectric constant $K$ has the same area as that of the plates of a parallel plate capacitor but has the thickness $d$, where $d$ is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

Q.

Why sign convection of outwards is cross and inwards in dot?

Q. The r.m.s value of electric field of the light coming from sun is $720N/C$. The average energy density of electromagnetic wave is

1. $3.3\times {10}^{-3}{J/m}^3$
2. $4.58\times {10}^{-6}{J/m}^3$
3. $6.37\times {10}^{-9}{J/m}^3$
4. $81.35\times {10}^{-12}{J/m}^3$

Q.

A 100 μF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?

(b) What is the time lag between the current maximum and the voltage maximum?

Q. Two point charges each having charge q are placed on the x axis at x=a and x=a. A. Plot the variation of electric field on the x axis B. Plot the variation of electric field on the y axis C. Find the position on the y axis where electric field is max

Q.

The nature of electromagnetic waves Z = is

1. longitudinal

2. longitudinal stationary

3. transverse

4. transverse stationery

Q.

In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10⁻³ m² and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

Q.

Explain briefly the process of charging a parallel plate capacitor when it is connected across a d.c. battery.

A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected?

(a) The electric field between the plates of the capacitor

(b) The energy stored in thecapacitor

Justify your answer by writing the necessary expressions

Q. Magnetic flux $\varphi$ in weber in a closed circuit of resistance $10\Omega$ varies with time $t$ (in seconds) as $\varphi =6t^2-5t+1$. The magnitude of induced current at $t=0.25\text{s}$ is

​​​​​​​$[$1 Mark$]$

1. $0.2\text{A}$
2. $0.6\text{A}$
3. $1.2\text{A}$
4. $0.8\text{A}$

Q. Two charges $4\times {10}^{-9}\text{C}$ and $-16\times {10}^{-9}\text{C}$ are separated by a distance $20\text{cm}$ in air. The position of the neutral point from the small charge is

1. $\frac{40}{3}\text{cm}$
2. $\frac{10}{3}\text{cm}$
3. $20\text{cm}$
4. $10\text{cm}$

Q.

Which among the following is a device that converts one form of energy into another :

1. Receiver

2. Transmitter

3. Transducer

4. Antenna

Q. Given below are two statements.

Statement I : A cyclotron is a device which is used to accelerate a charged particle.

Statement II: Cyclotron frequency depends upon the velocity.

Select the correct option.

1. Statements I and II are true, and Statement II is the correct explanation for Statement I
2. Statements I and II are true, and Statement II is not the correct explanation for Statement I
3. Statement I is true, but Statement II is false
4. Statement I is false, but Statement II is true

Q.

According to Maxwell’s hypothesis, a changing electric field gives rise to

1. An e.m.f.
2. Electric current
3. Magnetic field
4. Pressure radiant

Q. Define the term 'self-inductance' of a coil. Write its S.I. unit.

Q.

A point charge of 2 micro Coulomb is at the centre of a cubic Gaussian surface 9 cm on edge. What is the net electric flux through the surface?

Q.

The magnetic field of a plane electromagnetic wave is $\overrightarrow{B}=3\times {10}^{-8}\sin \left[200\mathrm{\pi }\left(\mathrm{y}+\mathrm{ct}\right)\right]\hat{i}T$ where$c=3\times {10}^{8}m{s}^{-1}$ is the speed of light . The corresponding electric field is

1. $\overrightarrow{E}=-9\sin \left[200\mathrm{\pi }\left(\mathrm{y}+\mathrm{ct}\right)\right]\hat{k}\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$

2. $\overrightarrow{E}=9\sin \left[200\mathrm{\pi }\left(\mathrm{y}+\mathrm{ct}\right)\right]\hat{k}\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$

3. $\overrightarrow{E}=-{10}^{-6}\sin \left[200\mathrm{\pi }\left(\mathrm{y}+\mathrm{ct}\right)\right]\hat{k}\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$

4. $\overrightarrow{E}=3\times {10}^{-8}\sin \left[200\mathrm{\pi }\left(\mathrm{y}+\mathrm{ct}\right)\right]\hat{k}\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$

Q. To which part of the electromagnetic spectrum does a wave of frequency $5\times {10}^{19}Hz$ belong?

Q.

A man crosses a 320 m wide river perpendicular to the current in 4 mm. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is

1. $30$

2. $40$

3. $50$

4. $60$

Q. The dimension of $LC$, where $L$ is the inductance and $C$ is the capacitance, is -

1. $\left[L\right]$
2. $\left[L^2\right]$
3. $\left[T\right]$
4. $\left[T^2\right]$

Q. Do electromagnetic waves carry energy and momentum ?

Q. For the given arrangement, a fixed finite line charge is kept in front of a block at equilibrium having $-10\text{nC}$ charge on it. Block and finite line charge are along same line. If in equilibrium, extension of spring is $10\text{cm}$ then spring constant $\left(K\right)$ is

1. $3000\text{N/m}$
2. $3500\text{N/m}$
3. $3375\text{N/m}$
4. $2575\text{N/m}$

Q. A rocket is going away from the earth at a speed $0.2c$, where c = speed of light. It emits a signal of frequency $4\times {10}^{7}Hz$. What will be the frequency observed by an observer on the earth?

1. $4\times {10}^{6}Hz$
2. $3.2\times {10}^{7}Hz$
3. $3\times {10}^{6}Hz$
4. $5\times {10}^{7}Hz$

Q. Find the energy stored in a $60\text{cm}$ length of a laser beam operating at $4\text{mW}$.

1. $8\times {10}^{-12}J$
2. $4\times {10}^{-12}J$
3. $8\times {10}^{-14}J$
4. $4\times {10}^{-4}J$