Electromagnetism PYQ — Page 48

A square loop of side $2a,$ and carrying current $I$ is kept in $XZ$ plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to the $z$-axis and passing through the point $(0,b,0),(b>>a)$. The magnitude of the torque on the loop about $z$-axis is given by.

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum:

Two capacitors of capacitances $C$ and $2C$ are charged to potential differences $V$ and $2V$, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

A solid sphere of radius $R$ carries a charge $Q+q$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$. If it acquires a speed $\nu$ when it has fallen through a vertical height $y$ (see figure), then (assume the remaining portion to be spherical) 

A circular coil of radius $10\mathrm{cm}$ is placed in a uniform magnetic field of $3.0\times {10}^{-5}T$ with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in $0.2s$. The maximum value of EMF induced (in $\mu V$) in the coil will be close to the integer....

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer $\text{G}$ attached across the coil?  Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $a$ and a concentric thin cylindrical shell of radius $b$ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $R$ will take place for : 

Two concentric circular coils, ${C}_{1}$ and ${C}_{2}$, are placed in the $XY$ plane. ${C}_{1}$ has $500$turns, and a radius of $1\mathrm{cm}$. ${C}_{2}$ has 200 turns and radius of $20\mathrm{cm}\text{.}{C}_{2}$ carries a time dependent current $I(t)=(5{t}^{2}-2t+3)A$ where $t$ is in s. The emf induced in ${C}_{1}(\mathrm{in}\mathrm{mV})$ at the instant $t=1$s is $\frac{4}{x}.$ The value of $x$ is ..........

A square loop of side $2a$ and carrying current $I$ is kept in $\mathrm{xz}$ plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to $z$-axis and passing through point $(0,b,0),(b>>a)$. The magnitude of torque on the loop about $z$-axis will be :

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$ . If a sphere of radius $\frac{R}{2}$ is carved out of it, as shown, the ratio $\frac{|\vec{{E}_{A}}|}{|\vec{{E}_{B}}|}$ of magnitude of electric field $\vec{{E}_{A}}$ and $\vec{{E}_{B}}$ , respectively, at points $A$ and $B$ due to the remaining portion is: 

For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is : $\vec{B}(x, t)=[1.2\times {10}^{-7}\mathrm{sin}(0.5\times {10}^{3}x+1.5\times {10}^{11}t)\hat{k}]T$. The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is :

A $10\mu F$ capacitor is fully charged to a potential difference of $50V$ After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20V$. The capacitance of the second capacitor is :

An electrical power line, having a total resistance of $2\Omega ,$ delivers $1\mathrm{kW}$ at $220V$. The efficiency of the transmission line is approximately :

A battery of $3.0\text{ V}$ is connected to a resistor dissipating $0.5\text{ W}$ of power. If the terminal voltage of the battery is $2.5\text{ V}$, the power dissipated within the internal resistance is:

A charged particle going around in a circle can be considered to be a current loop. A particle of a mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle is :

A charged particle (mass $m$ and charge $q$) moves along $X$ axis with velocity ${V}_{0}$. When it passes through the origin it enters a region having uniform electric field $\vec{E}=-E\hat{j}$ which extends upto $x=d$. Equation of path of electron in the region $x>d$ is: 

 A parallel plate capacitor has plates of area A separated by distance $d$ between them. It is filled with a dielectric which has a dielectric constant that varies as $K(x)={K}_{0}(1+\alpha x)$ where $x$ is the distance measured from one of the plates. If $(\alpha d)<<1,$ the total capacitance of the system is best given by the expression:

An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor $C$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length l. and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is 

The value of current ${i}_{1}$ flowing from $A$ to $C$ in the circuit diagram is : 

For the given input voltage waveform ${V}_{\text{in }}(t),$ the output voltage waveform ${V}_{0}(t),$ across the capacitor is correctly depicted by : 

Charges ${Q}_{1}$ and ${Q}_{2}$ are at points $A$ and $B$ of a right-angled triangle $OAB$. The resultant electric field at point $O$ is perpendicular to the hypotenuse, then ${Q}_{1}/{Q}_{2}$ is proportional to: 

A charge Q is distributed over two concentric conducting thin spherical shells radii $r$ and $R(R>r)$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is : 

In the circuit shown, charge on the $5\mu F$ capacitor is :