Electromagnetism PYQ

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are __________. 

A moving coil of galvanometer when shunted with $2\,\Omega$ resistance gives a full scale deflection for a current of $500$ mA. When a resistance of $470\,\Omega$ is connected in series it gives a full scale deflection for $10$ V potential applied on it. The value of resistance of galvanometer coil is __________ $\Omega$.

An electromagnetic wave travelling in $x$-direction is described by field equation $E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)$. If the electron is restricted to move in $y$-direction only with speed of $1.5 \times 10^6$ m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.

A small cube of side $1$ mm is placed at the centre of a circular loop of radius $10$ cm carrying a current of $2$ A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is _______. ($\mu_o = 4\pi \times 10^{-7}$ Tm/A, $\pi = 3.14$)

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1=E_0\hat{x}$. If another electric field $\vec{E}_2=2E_0(\hat{y}+\hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

The electric potential as a function of $x, y$ is given by $V = 5(x^2 - y^2)$ V. The electric field at a point $(2, 3)$ m is __________ V/m.

Under steady state condition the potential difference across the capacitor in the circuit is _______ V. 

A current of $30$ A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of $8$ cm. The magnetic field at the mid point between the two wires is __________ $\mu$T. $\left(\dfrac{\mu_0}{4\pi} = 10^{-7}\text{ N/A}^2\right)$

Two resistors of $200 \, \Omega$ and $400 \, \Omega$ are connected in series with a battery of $100$ V. A bulb rated at $200$ V, $100$ W is connected across the $400 \, \Omega$ resistance. The potential drop across the bulb is _______ V.

Two point charges $q_1=3\,\mu C$ and $q_2=-4\,\mu C$ are placed at points $(2\hat{i}+3\hat{j}+3\hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge $q_2$ is ________ N. $\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^9 \text{ SI Units}\right)$

Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse - square force. D. The workdone in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :

A circular current loop of radius $R$ is placed inside square loop of side length $L$ $(L >> R)$ such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between circular loop and square loop is _______.

An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 V. The percentage efficiency of transmission line is $\_\_\_\_$ .

The electric field in a plane electromagnetic wave is given by : $E_{y}=69 \sin \left[0.6 \times 10^{3} x-1.8 \times 10^{11} t\right] \mathrm{V} / \mathrm{m}$. The expression for magnetic field associated with this electromagnetic wave is $\_\_\_\_$ T.

A circular coil of radius $2$ cm and $125$ turns carries a current of $1$ A. The coil is placed in a uniform magnetic field of magnitude $0.4$ T. The axis of the coil makes an angle of $30°$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4}$ N.m. The value of $\alpha$ is ______. ($\pi=3.14$)

$1\,\mu$C charge moving with velocity $\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$ m/s in the region of magnetic field $\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{-6}$ N. The value of $\alpha$ is _______.

A charged particle moves in a uniform magnetic field. If the velocity is perpendicular to the field, the path of the particle is:

A square loop of side $2$ cm is placed in a time varying magnetic field with magnitude as $B = 0.4\sin(300t)$ Tesla. The normal to the plane of loop makes an angle of $60°$ with the field. The maximum induced emf produced in the loop is __________ mV.

Three identical coils $C_{1}, C_{2}$ and $C_{3}$ are closely placed such that they share a common axis. $C_{2}$ is exactly midway. $C_{1}$ carries current $I$ in anti-clockwise direction while $C_{3}$ carries current $I$ in clockwise direction. An induced current flows through $C_{2}$ will be in clockwise direction when

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V=5 \sin (100 t)$ The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor (C) used is $\_\_\_\_$ $\mu \mathrm{F}$. 

Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ($k_{1}$ and $k_{2}$) in the following fashion. Which of the following is true? $\left(k_{1}>k_{2}\right)$