Electromagnetism PYQ — Page 65

A charge $Q$ is uniformly distributed over the surface of non conducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure

Three positive charges of equal value $q$ are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in

A coil of self inductance $L$ is connected at one end of two rails as shown in figure. A connector of length $l$, mass $m$ can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction $B$ going into the page. At an instant $t=0$ an initial velocity $v_0$ is imparted to it and as a result of that it starts moving along $x$-axis. The displacement of the connector is represented by the figure. 

Three resistors of $4 \Omega, 6 \Omega$ and $12 \Omega$ are connected in parallel and the combination is connected in series with a $1.5 \mathrm{~V}$ battery of $1 \Omega$ internal resistance. The rate of Joule heating in the $4 \Omega$ resistor is

The magnetic force acting on charged particle of charge $2 \mu \mathrm{C}$ in magnetic field of $2 T$ acting in $y-$ direction, when the particle velocity is $(2 \hat{i}+3 \hat{j}) \times 10^6 \mathrm{~ms}^{-1}$ is

In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be

Magnetic flux through a coil of resistance $10 \Omega$ is changed by $\Delta \phi$ in $0.1 \mathrm{~s}$. The resulting current in the coil varies with time as shown in the figure. Then $|\Delta \phi|$ is equal to (in weber) 

An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\vec{X}$ and that of wave propagation by $\overrightarrow{\mathrm{k}}$. Then :

A resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t=$ 0 . If after $t$ sec the voltage across the capacitance was seven times the voltage across $\mathrm{R}$, the value of $\mathrm{t}$ is

Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires $A$ and $B$ respectively in opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2 \mathrm{~m}$. The force acting on the conductor $B$, which is situated at $10 \mathrm{~cm}$ distance from $A$ will be

An electromagnetic wave with frequency $\omega$ and wavelength $\lambda$ travels in the $+y$ direction. Its magnetic field is along $+x$-axis. The vector equation for the associated electric field (of amplitude $E_0$ ) is

The electric potential $V(x)$ in a region around the origin is given by $V(x)=4 x^2$ volts. The electric charge enclosed in a cube of $1 \mathrm{~m}$ side with its centre at the origin is (in coulomb)

A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius $R$, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be

A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \mathrm{NA}^{-1} \mathrm{~m}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2 \mathrm{~m}$ long. If the speed of the boat is $1.50 \mathrm{~ms}^{-1}$, the magnitude of the induced emf in the wire of aerial is :

The electrostatic potential inside a charged spherical ball is given by $\phi=\alpha \rho^2+b$ where $r$ is the distance from the centre; $a, b$ are constants. Then the charge density inside ball is

Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance $d(d< < 1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,

A resistor 'R' and $2 \mu \mathrm{F}$ capacitor in series is connected through a switch to $200 \mathrm{~V}$ direct supply. Across the capacitor is a neon bulb that lights up at $120 \mathrm{~V}$. Calculate the value of $R$ to make the bulb light up $5 \mathrm{~s}$ after the switch has been closed. $\left(\log _{10} 2.5=0.4\right)$

A fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is :

A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius $\mathrm{R}$. The magnitude of the magnetic induction along its axis is

Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r)=\rho_0\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho(r)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r(r < R)$ from the origin is given by

Let $C$ be the capacitance of a capacitor discharging through a resistor R. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1 / t_2$ will be

Two long parallel wires are at a distance $2 \mathrm{~d}$ apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line $\mathrm{XX}$ ' is given by

A rectangular loop has a sliding connector PQ of length $\ell$ and resistance $\mathrm{R} \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are 

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \mathrm{~g} \mathrm{~cm}^{-3}$, the angle remains the same. If density of the material of the sphere is $16 \mathrm{~g} \mathrm{~cm}^{-3}$, the dielectric constant of the liquid is