Electromagnetism PYQ — Page 13

Equivalent resistance of the following network is ________ $\Omega$. 

The electric field at point $\mathrm{p}$ due to an electric dipole is $\mathrm{E}$. The electric field at point $\mathrm{R}$ on equitorial line will be $\frac{\mathrm{E}}{x}$. The value of $x$ : 

An electron with kinetic energy $5 \mathrm{eV}$ enters a region of uniform magnetic field of 3 $\mu \mathrm{T}$ perpendicular to its direction. An electric field $\mathrm{E}$ is applied perpendicular to the direction of velocity and magnetic field. The value of $E$, so that electron moves along the same path, is _______ $\mathrm{NC}^{-1}$. $\left(\right.$ Given, mass of electron $=9 \times 10^{-31} \mathrm{~kg}$, electric charge $\left.=1.6 \times 10^{-19} \mathrm{C}\right)$

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

A power transmission line feeds input power at $2.3\mathrm{kV}$ to a step down transformer with its primary winding having $3000\text{turns}$. The output power is delivered at $230V$ by the transformer. The current in the primary of the transformer is $5A$ and its efficiency is $90%$. The winding of transformer is made of copper. The output current of transformer is ____$A$.

The reading in the ideal voltmeter $(V)$ shown in the given circuit diagram is: 

A plane EM wave is propagating along $x$ direction. It has a wavelength of $4 \mathrm{~mm}$. If electric field is in $y$ direction with the maximum magnitude of $60 \mathrm{Vm}^{-1}$, the equation for magnetic field is :

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across $A$ and $B$, their readings are ${V}_{1},{V}_{2}$ and ${V}_{3}$. Choose the correct option. 

When a $d c$ voltage of $100 \mathrm{~V}$ is applied to an inductor, a $d c$ current of $5 \mathrm{~A}$ flows through it. When an ac voltage of $200 \mathrm{~V}$ peak value is connected to inductor, its inductive reactance is found to be $20 \sqrt{3} \Omega$. The power dissipated in the circuit is _______ W.

Match List I with List II <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>A.</td><td>Gauss’s law of magnetostatics</td><td>i.</td><td>$\oint \vec{E}\cdot d\vec{a}=\frac{1}{{\epsilon }_{0}}\int \rho dV$</td></tr><tr><td>B.</td><td>Faraday’s law of electro magnetic induction</td><td>ii.</td><td>$\oint \vec{B}\cdot d\vec{a}=0$</td></tr><tr><td>C.</td><td>Ampere’s law</td><td>iii.</td><td>$\oint \vec{E}\cdot d\vec{l}=\frac{-d}{dt}\int \vec{B}\cdot d\vec{a}$</td></tr><tr><td>D.</td><td>Gauss’s law of electrostatics</td><td>iv.</td><td>$\oint \vec{B}\cdot d\vec{l}={\mu }_{0}I$</td></tr></tbody></table>Choose the correct answer from the options given below:

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ from axis of the wire is :

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha [\frac{ql}{{r}^{2}}]\times {10}^{9}V$, where the value of $\alpha$ is ______. (Use $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$) 

Two cells are connected in opposition as shown. Cell ${E}_{1}$ is of $8V$ emf and $2\Omega$ internal resistance; the cell ${E}_{2}$ is of $2V$ emf and $4\Omega$ internal resistance. The terminal potential difference of cell ${E}_{2}$ is ______ $V$. 

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $1 / \theta$ vs the resistance $(\mathrm{R})$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is _____ $\times 10^{-1} \mathrm{~A} /$ division. [The source has emf 2V] 

A coil is placed perpendicular to a magnetic field of $5000T$. When the field is changed to $3000T$ in $2s$, an induced emf of $22V$ is produced in the coil. If the diameter of the coil is $0.02m$, then the number of turns in the coil is:

In a coil, the current changes from $-2 \mathrm{~A}$ to $+2 \mathrm{~A}$ in $0.2 \mathrm{~s}$ and induces an emf of $0.1 \mathrm{~V}$. The self inductance of the coil is :

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8\Omega$ varies with time (in seconds) as $\phi =5{t}^{2}-36t+1$. The induced current in the circuit at $t=2s$ is _______ $A$.

In the given circuit, the current in resistance ${R}_{3}$ is: 

A galvanometer has a resistance of $50\Omega$ and it allows maximum current of $5\mathrm{mA}$. It can be converted into voltmeter to measure upto $100V$ by connecting in series a resistor of resistance.

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

An object is placed in a medium of refractive index $3$. An electromagnetic wave of intensity $6\times {10}^{8}W{m}^{-2}$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $=3\times {10}^{8}m{s}^{-1}$ ):

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$. The relative permeability of the medium is 2.0 . The relative permittivity will be:

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B={B}_{0}\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is : 

A moving coil galvanometer has $100$ turns and each turn has an area of $2.0{\mathrm{cm}}^{2}.$ The magnetic field produced by the magnet is $0.01T$ and the deflection in the coil is $0.05$ radian when a current of $10\mathrm{mA}$ is passed through it. The torsional constant of the suspension wire is $x\times {10}^{-5}N-m/\mathrm{rad}.$ The value of $x$ is ______ .