Electromagnetism PYQ — Page 14

The magnetic field existing in a region is given by $\vec{B}=0.2(1+2 x) \hat{k} \mathrm{~T}$. A square loop of edge $50 \mathrm{~cm}$ carrying 0.5 A current is placed in $x-y$ plane with its edges parallel to the $x-y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is_____ $\mathrm{mN}$. 

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii ${R}_{1}=2\pi m$ and ${R}_{2}=4\pi m$ carrying current $I=4A$ as per figure given below is $\alpha \times {10}^{-7}T$. The value of $\alpha$ is _____. (Centre $O$ is common for all segments) 

The horizontal component of earth's magnetic field at a place is $3.5\times {10}^{-5}T$. A very long straight conductor carrying current of $\sqrt{2}A$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________$\times {10}^{-6}N{m}^{-1}$.

The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is : 

The electrostatic potential due to an electric dipole at a distance $r$ varies as :

The electrostatic force $\left(\overrightarrow{F_1}\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written :

The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9\times {10}^{-13}\mathrm{cm}$ is $\alpha \times {10}^{6}V$. What is the value of $\alpha$? (Charge of proton $1.6\times {10}^{-19}C$)

The electric field of an electromagnetic wave in free space is represented as $\vec{E}={E}_{0}\mathrm{cos}(\omega t-kz)\hat{i}$. The corresponding magnetic induction vector will be :

The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t}-z / \mathrm{c}) \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit) :

The electric field between the two parallel plates of a capacitor of $1.5 \mu \mathrm{F}$ capacitance drops to one third of its initial value in $6.6 \mu \mathrm{s}$ when the plates are connected by a thin wire. The resistance of this wire is _____$\Omega$. (Given, $\log 3=1.1$ )

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 $x$ : 

The electric current through a wire varies with time as $I={I}_{0}+\beta t$, where ${I}_{0}=20A$ and $\beta =3A{s}^{-1}$. The amount of electric charge crossed through a section of the wire in $20s$ is:

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be 

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 $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$) 

The deflection in moving coil galvanometer falls from $25$ divisions to $5$ division when a shunt of $24\Omega$ is applied. The resistance of galvanometer coil will be:

The current of $5A$ flows in a square loop of sides $1m$ is placed in air. The magnetic field at the centre of the loop is $X\sqrt{2}\times {10}^{-7}T$. The value of $X$ is _________.

The current in an inductor is given by $\mathrm{I}=(3 \mathrm{t}+8)$ where $\mathrm{t}$ is in second. The magnitude of induced emf produced in the inductor is $12 \mathrm{mV}$. The self-inductance of the inductor _____ $\mathrm{mH}$.

The current in a conductor is expressed as $I=3{t}^{2}+4{t}^{3}$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1s$ to $t=2s$ is ____________ $C.$

The current flowing through the $1 \Omega$ resistor is $\frac{n}{10}$ A. The value of $n$ is _________ 

The coercivity of a magnet is $5 \times 10^3 \mathrm{~A} / \mathrm{m}$. The amount of current required to be passed in a solenoid of length $30 \mathrm{~cm}$ and the number of turns 150 , so that the magnet gets demagnetised when inside the solenoid is _____A.

The charge accumulated on the capacitor connected in the following circuit is ______\mu C. (Given $C=150\mu F)$ 

Suppose a uniformly charged wall provides a uniform electric field of $2\times {10}^{4}N{C}^{-1}$ normally. A charged particle of mass $2g$ being suspended through a silk thread of length $20\mathrm{cm}$ and remain stayed at a distance of $10\mathrm{cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}}\mu C$ where $x=$ ________ [use $g=10m{s}^{-2}$]

Resistance of a wire at $0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$ and $t^{\circ} \mathrm{C}$ is found to be $10 \Omega, 10.2 \Omega$ and $10.95 \Omega$ respectively. The temperature $t$ in Kelvin scale is _________

Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :