Electromagnetism PYQ — Page 7

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $10 \pi \mathrm{rad} \mathrm{s}^{-1}$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? $(\pi=3.14)$

A current of 5A exists in a square loop of side $\frac{1}{\sqrt{2}} \mathrm{~m}$. Then the magnitude of the magnetic field $B$ at the centre of the square loop will be $p \times 10^{-6} \mathrm{~T}$. where, value of p is _____ . $\left[\right.$ Take $\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$.

An infinitely long wire has uniform linear charge density $\lambda=2 \mathrm{nC} / \mathrm{m}$. The net flux through a Gaussian cube of side length $\sqrt{3} \mathrm{~cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $\mathrm{xNm}^2 \mathrm{C}^{-1}$, where x is : [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ SI units]

A small bob of mass 100 mg and charge $+10 \mu \mathrm{C}$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be : (Given, $\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}$ and acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$) 

Four capacitor each of capacitance $16 \mu \mathrm{~F}$ are connected as shown in the figure. The capacitance between points A and B is : ______ (in $\mu \mathrm{F}$). 

Two metal spheres of radius $R$ and $3 R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is.

A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1=6 \pi \mathrm{~m}$ and $\mathrm{R}_2=4 \pi \mathrm{~m}$. The magnitude of the resultant magnetic field at center O is $\mathrm{k} \times 10^{-7} \mathrm{~T}$. The value of k is ______ (Given $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$) 

A line charge of length $\frac{\text { ' } a \text { ' }}{2}$ is kept at the center of an edge $B C$ of a cube $A B C D E F G H$ having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda$ C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, $\epsilon_0$ as the free space permittivity) 

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $\varepsilon_1$ and $\varepsilon_2$, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $C_1$ and $C_2$ respectively, then $\frac{C_1}{C_2}$ is :  

Two long parallel wires $X$ and $Y$, separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $x \times 10^{-5} \mathrm{~T}$. The value of $x$ is__________ . Take permeability of free space as $\mu_0=4 \pi \times 10^{-7} \mathrm{SI}$ units. 

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity $10^6 \mathrm{~m} / \mathrm{s}$. If the magnitude of the electric field between the plates is $9.1 \mathrm{~V} / \mathrm{cm}$, then the vertical component of velocity of electron is (mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ and charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ )

Find the equivalent resistance between two ends of the following circuit 

An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

Conductor wire ABCDE with each $\operatorname{arm} 10 \mathrm{~cm}$ in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of $10 \mathrm{~cm} / \mathrm{s}$, induced emf between points A and E is _____ mV. 

An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

Given below are two statements: one is labelled as Assertion A and the other is labelled asReason R. Assertion A:. If oxygen ion $\left(\mathrm{O}^{-2}\right)$ and Hydrogen ion $\left(\mathrm{H}^{+}\right)$enter normal to the magnetic field with equal momentum, then the path of $\mathrm{O}^{-2}$ ion has a smaller curvature than that of $\mathrm{H}^{+}$. Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statements, choose the correct answer from the options given below :

An alternating current is represented by the equation, $i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

A galvanometer having a coil of resistance $30 \Omega$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X} \Omega$, where $X$ is Options

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is $91.6 \%$, then the loss of power in units of $\mathrm{cal} / \mathrm{s}$ is

A particle of charge $q$, mass $m$ and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius( r). Which of the following curves represents the variation of $r$ with $E$ ?

A magnetic dipole experiences a torque of $80 \sqrt{3} \mathrm{~N} \mathrm{~m}$ when placed in uniform magnetic field in such a way that dipole moment makes angle of $60^{\circ}$ with magnetic field. The potential energy of the dipole is :

An ac current is represented as $\mathrm{i}=5 \sqrt{2}+10 \cos \left(650 \pi \mathrm{t}+\frac{\pi}{6}\right) \mathrm{Amp}$ The r.m.s value of the current is

The magnitude of force on a charge q moving with velocity v in a magnetic field B at angle θ is: