Electromagnetism PYQ — Page 2

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4 R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is : (Take $k=\frac{1}{4 \pi \epsilon_{0}}$ and assume $k Q^{2}>G m^{2}$ where $G$ is the Gravitational constant)

Figure shows the circuit that contains three resistances ($9 \Omega$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch $K$ is turned ON, is $\_\_\_\_$ A. 

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25 \%$ more charge from the battery. The dielectric constant of mica is $\_\_\_\_$.

A sphere of capacitance $100$ pF is charged to a potential of $100$ V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}$ J. The value of $\alpha$ is __________. (combined capacitance of spheres is $200$ pF)

Match the LIST-I with LIST-II \(\begin{array}{|l|l|l|l|} \hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Radio-wave} & \text{I.} & \text{is produced by Magnetron valve} \\ \hline \text{B.} & \text{Micro-wave} & \text{II.} & \text{due to change in the vibrational modes of atoms} \\ \hline \text{C.} & \text{Infrared-wave} & \text{III.} & \text{due to inner shell electrons moving from higher to lower energy level} \\ \hline \text{D.} & \text{X-ray} & \text{IV.} & \text{due to rapid acceleration of electrons} \\ \hline \end{array}\) Choose the correct answer from the options given below:

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is $\_\_\_\_$ mV. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

A capacitor $C$ is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance $L$. In $t \mathrm{~s} \ 25 \%$ of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is $\_\_\_\_$ s.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material : Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains. Reason (R): At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature. In the light of the above statements, choose the correct answer from the options given below :

Three identical coils $C_{1}, C_{2}$ and $C_{3}$ are closely placed such that they share a common axis. $C_{2}$ is exactly midway. $C_{1}$ carries current $I$ in anti-clockwise direction while $C_{3}$ carries current $I$ in clockwise direction. An induced current flows through $C_{2}$ will be in clockwise direction when

Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10 \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^{2}} \mathrm{~J} / \mathrm{m}^{3}$. The value of $\alpha$ is $\_\_\_\_$. ($\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$).

Identify the correct statements : A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below :

For the series $L C R$ circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$. 

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ($g=10 \mathrm{~m} / \mathrm{s}^{2}$) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of 200 m is $\_\_\_\_$ mV.

Two short electric dipoles $A$ and $B$ having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60°$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is _______. 

Match List - I with List - II. $\begin{array}{l} \text{List - I} & \text{List - II} \\ \text{Relation} & \text{Law} \\ \text{A. } \oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d a} & \text{I. Ampere's circuital law} \\ \text{B. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0}\left(I+\epsilon_{0} \frac{d \phi_{E}}{d t}\right) & \text{II. Faraday's laws of} \\ & \text{electromagnetic induction} \\ \text{C. } \oint \vec{E} \cdot \overrightarrow{d a}=\frac{1}{\epsilon_{0}} \int_{\mathrm{V}} \rho \mathrm{dv} & \text{III. Ampere - Maxwell law} \\ \text{D. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I & \text{IV. Gauss's law of electrostatics} \end{array}$ Choose the correct answer from the options given below :

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t / T)$. The r.m.s current for the period $t=0$ to $t=T$ is $\_\_\_\_$.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is _____.

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire $Q$ is $\_\_\_\_$.  ($\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{~T}. \mathrm{m} / \mathrm{A}$)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In electrostatics, a conductor does not store any net charge inside. Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift. Choose the correct answer from the options given below

The electrostatic potential in a charged spherical region of radius $r$ varies as $V=a r^{3}+b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha \times \pi a \in_{\mathrm{o}}$. The value of $\alpha$ is $\_\_\_\_$. (permittivity of vacuum is $\epsilon_{0}$)

Three charges $+2 q,+3 q$ and $-4 q$ are situated at $(0,-3 a),(2 a, 0)$ and $(-2 a, 0)$ respectively in the $x y$ plane. The resultant dipole moment about origin is $\_\_\_\_$.

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque of $0.016 \mathrm{~N}. \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$.

Two known resistances of $R \Omega$ and $2 R \Omega$ and one unknown resistance $X \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X \Omega$, then the value of $X$ is $\_\_\_\_$ $\Omega$. 

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $E_{\mathrm{y}}=20 \sin \left(3 \times 10^{6} x-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m}$ (where $x, \mathrm{t}$ and other values have S.I. units). The dielectric constant of the medium is $\_\_\_\_$ (speed of light in free space is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$)