Electromagnetism PYQ — Page 57

An ideal capacitor of capacitance $0.2 \mu \mathrm{F}$ is charged to a potential difference of $10 \mathrm{~V}$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5 \mathrm{mH}$. The current at a time when the potential difference across the capacitor is $5 \mathrm{~V}$, is:

At the centre of a fixed large circular coil of radius $\mathrm{R}$, a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation.

On interchanging the resistances, the balance point of a meter bridge shifts to the left by $10\mathrm{cm}$. The resistance of their series combination is $1k\Omega$ . How much was the resistance on the left slot before interchanging the resistances?

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $\rho$, how long will the charges take to travel a distance $\mathrm{d}$ ?

A charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to normal axis then magnetic moment of the loop is:

In a meter bridge as shown in the figure, it is given that resistance $Y=12.5\Omega$ and that the balance is obtained at a distance $39.5\mathrm{cm}$ from end $A$ (by jockey $J$). After interchanging the resistances $X$ and $Y$ a new balance point is found at a distance ${l}_{2}$ from end $A$. What are the values of $X$ (in $\Omega$) and ${l}_{2}$? 

A charge $Q$ is placed at a distance $\mathrm{a} / 2$ above the centre of the square surface of edge a as shown in the figure. The electric flux through the square surface is: 

A monochromatic beam of light has a frequency $v=\frac{3}{2 \pi} \times 10^{12} \mathrm{~Hz}$ and is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$. It is polarized along the $\hat{k}$ direction. The acceptable form for the magnetic field is:

A current of $1 \mathrm{~A}$ is flowing on the sides of an equilateral triangle of side $4.5 \times 10^{-2} \mathrm{~m}$. The magnetic field at the centre of the triangle will be:

A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I={I}_{0}\mathrm{cos}⁡(\omega t).$ The emf induced in the smaller inner loop is nearly:

The electric field component of a monochromatic radiation is given by $\vec{E}=2{E}_{0}\mathrm{cos}kz\mathrm{cos}\omega t\hat{i}$, Its magnetic field $\vec{B}$ is then given by:

A uniform magnetic field $B$ of $0.3T$ is along the positive $\text{Z}$ -direction. A rectangular loop ($abcd$) of sides $10 \mathrm{cm}\times 5 \mathrm{cm}$ carries a current $I$ of $12A$. Out of the following different orientations which one corresponds to stable equilibrium?

In the given circuit diagram, when the current reaches a steady-state in the circuit, the charge on the capacitor of capacitance $C$ will be: 

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $X-$rays. It produces continuous as well as characteristic $X-$rays. If ${\lambda }_{min}$ is the smallest possible wavelength of $X-$ray in the spectrum, the variation of $\mathrm{log}({\lambda }_{min})$ with $\mathrm{log}(V)$ is correctly represented in :

Four closed surfaces and corresponding charge distributions are shown below.  Let the respective electric fluxes through the surfaces be ${\phi }_{1}, {\phi }_{2}, {\phi }_{3}$ and ${\phi }_{4}$. Then:

A capacitance of $2 \mu F$ is required in an electrical circuit across a potential difference of $1\text{.}0\mathrm{kV}$. A large number of $1 \mu F$ capacitors are available which can withstand a potential difference of not more than $300V$. The minimum number of capacitors required to achieve this is:

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec{B}={B}_{0}(\hat{i}+2\hat{j}-4\hat{k})$. If a test charge moving with a velocity $\vec{v}={v}_{0}(3\hat{i}-\hat{j}+2\hat{k})$ experiences no force in that region, then the electric field in the region, in SI units, is:

A sinusoidal voltage of peak value $283V$ and angular frequency $320{s}^{-1}$ is applied to a series $LCR$ circuit. Given that $R=5 \Omega , L=25 \mathrm{mH}$ and $C=1000\mu F$. The total impedance and phase difference between the voltage across the source and the current will respectively be-

 In the above circuit the current in each resistance is:

The energy stored in the electric field produced by a metal sphere is $4.5J$. If the sphere contains $4\mu C$ charge, its radius will be: $[Take:\frac{1}{4\pi {\in }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}]$

The figure shows three circuits $I, II$ and $III$ which are connected to a $3V$ battery. If the powers dissipated by the configurations $I, II$ and $III$ are ${P}_{1}, {P}_{2}$ and ${P}_{3}$ respectively, then - 

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P=4 \Omega$ and the neutral point $N$ is at $60\mathrm{cm}$ from $A$ . Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80\mathrm{cm}$ from $A$ . The value of unknown resistance $R$ is - 

 A $9V$ battery with an internal resistance of $0.5 \Omega$ is connected across an infinite network, as shown in the figure. All ammeters ${A}_{1}, {A}_{2}, {A}_{3}$ and voltmeter $V$ are ideal. Choose the correct statement.

An electric dipole has fixed dipole moment $\vec{p}$, which makes angle $\theta$ with respect to $x-$axis. When subjected to an electric field ${\vec{E}}_{1}=E\hat{i},$ it experiences a torque ${\vec{T}}_{1}=\tau \hat{k}$. When subjected to another electric field ${\vec{E}}_{2}= \sqrt{3} {E}_{1}\hat{j}$ it experiences a torque ${\vec{T}}_{2}=-{\vec{T}}_{1}$ . The angle $\theta$ is: