Electromagnetism PYQ — Page 15

The magnetic field in a plane electromagnetic wave is $\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{T}$. The corresponding electric field will be :

A proton and a deutron ( $q=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:

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 ____________ $C.$

A heater is designed to operate with a power of $1000 \mathrm{~W}$ in a $100 \mathrm{~V}$ line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a $100 \mathrm{~V}$ mains as shown in figure. For the heater to operate at $62.5 \mathrm{~W}$, the value of $\mathrm{R}$ should be _____$\Omega$. 

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:

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

Wheatstone bridge principle is used to measure the specific resistance $({S}_{1})$ of given wire, having length $L$, radius $r$. If $X$ is the resistance of wire, then specific resistance is : ${S}_{1}=X(\frac{\pi {r}^{2}}{L})$. If the length of the wire gets doubled then the value of specific resistance will be :

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5g/\mathrm{cc},$ the dielectric constant of water will be ______. (Take density of water $=1g/\mathrm{cc}$)

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3} \mathrm{~m}^2$ and resistance $100 \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $\mathrm{B}=0.5 \mathrm{~T}$ as shown. Work done in pulling the loop out of the field in $1.0 \mathrm{~s}$ is ______ $\times 10^{-6} \mathrm{~J}$. 

Arrange the following in the ascending order of wavelength: A. Gamma rays $\left(\lambda_1\right)$ B. $x$ - rays $\left(\lambda_2\right)$ C. Infrared waves $\left(\lambda_3\right)$ D. Microwaves $\left(\lambda_4\right)$ Choose the most appropriate answer from the options given below

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm $\mathrm{BC}$ is made up of the semiconductor. The experiment is being conducted at $25^{\circ}C$ and resistance of the semiconductor arm is $3m\Omega$. Arm $\mathrm{BC}$ is cooled at a constant rate of $2^{\circ}C{s}^{-1}$. If the galvanometer $G$ shows no deflection after $10s,$ then $\alpha$ is: 

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 _________

Two charges $q$ and $3q$ are separated by a distance ‘$r$’ in air. At a distance $x$ from charge $q$, the resultant electric field is zero. 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 _____ $\mathrm{mH}$.

A series LCR circuit with $L=\frac{100}{\pi }\mathrm{mH},C=\frac{{10}^{-3}}{\pi }F$ and $R=10\Omega$, is connected across an AC source of $220V,50\mathrm{Hz}$ supply. The power factor of the circuit would be ____.

Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below:

Two charges of $-4\mu C$ and $+4\mu C$ are placed at the points $A(1,0,4)m$ and $B(2,-1,5)m$ located in an electric field $\vec{E}=0.20\hat{i}V{\mathrm{cm}}^{-1}$. The magnitude of the torque acting on the dipole is $8\sqrt{\alpha }\times {10}^{-5}Nm$, where $\alpha =$_________.

A coil having 100 turns, area of $5 \times 10^{-3} \mathrm{~m}^2$, carrying current of $1 \mathrm{~mA}$ is placed in uniform magnetic field of $0.20 \mathrm{~T}$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ}$ is _______ $\mu \mathrm{J}$.

An element $\Delta l=\Delta x \hat{i}$ is placed at the origin and carries a large current $I=10 \mathrm{~A}$. The magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m}$ from the elements $\Delta x$ of $1 \mathrm{~cm}$ length is: 

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below :

A rectangular loop of length $2.5m$ and width $2m$ is placed at $60^{\circ}$ to a magnetic field of $4T$. The loop is removed from the field in $10\mathrm{sec}$. The average emf induced in the loop during this time is

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 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_____ $\mathrm{mN}$. 

A $16\Omega$ wire is bend to form a square loop. A $9V$ battery with internal resistance $1\Omega$ is connected across one of its sides. If a $4\mu F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2}\mu J$, where $x=$______.