Electromagnetism PYQ — Page 41

The equivalent resistance of the given circuit between the terminals $A$ and $B$ is : 

A coaxial cable consists of an inner wire of radius $a$ surrounded by an outer shell of inner and outer radii $b$ and $c$ respectively. The inner wire carries an electric current ${i}_{0}$ which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance $x$ from the axis when $(i)$ $x<a$ and $(ii)$ $a<x<b$ ?

The fractional change in the magnetic field intensity at a distance $r$ from centre on the axis of current carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r<a$)

A cell ${E}_{1}$ of emf $6V$ and internal resistance $2\Omega$ is connected with another cell ${E}_{2}$ of emf $4V$ and internal resistance $8\Omega$ (as shown in the figure). The potential difference across points $X$ and $Y$ is: 

A $0.07H$ inductor and a $12\Omega$ resistor are connected in series to a $220V,50\mathrm{Hz}$ AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as $\frac{22}{7}]$

Consider an electrical circuit containing a two way switch $S.$ Initially $S$ is open and then ${T}_{1}$ is connected to ${T}_{2}.$ As the current in $R=6\Omega$ attains a maximum value of steady-state level, ${T}_{1}$ is disconnected from ${T}_{2}$ and immediately connected to ${T}_{3}.$ Potential drop across $r=3\Omega$ resistor immediately after ${T}_{1}$ is connected to ${T}_{3}$ is $______V.$ (Round off to the Nearest Integer) 

A light beam is described by $E=800\mathrm{sin}\omega (t-\frac{x}{c}).$ An electron is allowed to move normal to the propagation of light beam with a speed of $3\times {10}^{7}{ms}^{-1}$. What is the maximum magnetic force exerted on the electron?

A current of $5A$ is passing through a non-linear magnesium wire of cross-section $0.04{m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (resistivity of magnesium $\rho =44\times {10}^{-8}\Omega m$)

Two cells of emf $2E$ and $E$ with internal resistance ${r}_{1}$and ${r}_{2}$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R,$ at which the potential difference across the terminals of the first cell becomes zero is 

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric $({U}_{e})$ and magnetic $({U}_{m})$ fields is :

In an electromagnetic wave, the electric field vector and magnetic field vector are given as $\vec{E}={E}_{0}\hat{i}$ and $\vec{B}={B}_{0}\hat{k}$, respectively. The direction of propagation of electromagnetic wave is along:

The wavelength of an X-ray beam is $10Å$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3}h\mathrm{kg}.$ The value of $x$ is ___ . ($h=$Planck's constant)

The magnetic field vector of an electromagnetic wave is given by $B={B}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\mathrm{cos}(kz-\omega t)$ where $\hat{i},\hat{j}$ represents unit vector along $x$ and $y$-axis respectively. At $t=0s,$ two electric charges ${q}_{1}$ of $4\pi$ coulomb and ${q}_{2}$ of $2\pi$ coulomb located at $(0,0,\frac{\pi }{k})$ and $(0,0,\frac{3\pi }{k}),$ respectively, have the same velocity of $0.5c\hat{i},$ (where $c$ is the velocity of light ). The ratio of the force acting on charge ${q}_{1}$ to ${q}_{2}$ is :

$27$ similar drops of mercury are maintained at $10V$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________ times that of a smaller drop.

A parallel plate capacitor has plate area $100{m}^{2}$ and plate separation of $10m.$ The space between the plates is filled up to a thickness $5m$ with a material of dielectric constant of $10.$ The resultant capacitance of the system is $x\mathrm{pF}.$ The value of ${\epsilon }_{0}=8.85\times {10}^{-12}F{m}^{-1}$. The value of $x$ to the nearest integer is ______.

An alternating current is given by the equation $i={i}_{1}\mathrm{sin}\omega t+{i}_{2}\mathrm{cos}\omega t$. The rms current will be:

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b.$ Identify the graph showing the variation of different quantities with distance:  

A coil is placed in a magnetic field $\vec{B}$ as shown below :  A current is induced in the coil because $\vec{B}$ is :

For changing the capacitance of a given paralle plate capacitor, a dielectric material of dielectric constant $K$ is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4}d$, where $d$ is the separation between the plates of parallel plate capacitor. The new capacitance ${C}^{'}$ in terms of original capacitance ${C}_{0}$ is given by the following relation :

Following plots show Magnetization $(M)$ vs Magnetising field $(H)$ and Magnetic susceptibility $(\chi )$ vs Temperature $(T)$ graph :  Which of the following combination will be represented by a diamagnetic material?

Two wires of same length and thickness having specific resistances $6\Omega \mathrm{cm}$ and $3\Omega \mathrm{cm}$ respectively are connected in parallel. The effective resistivity is $\rho \Omega cm$. The value of $\rho$ to the nearest integer, is ___ .

For full scale deflection of total $50$ divisions, $50\mathrm{mV}$ voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is $2\mathrm{div}/\mathrm{mA}$ will be:

A transmitting station releases waves of wavelength $960m$. A capacitor of $2.56\mu F$ is used in the resonant circuit. The self-inductance of coil necessary for resonance is $x\times {10}^{-8}H$. find $x$

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05m$ and $0.2m$ from the centre are in the ratio $8:1$. The radius of coil is _______ .