Electromagnetism PYQ — Page 3

Two metal plates $(A, B)$ are kept horizontally with separation of $\left(\dfrac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density $1.5$ g/cm$^3$) droplets of radius $1$ mm horizontally. All oil droplets carry a charge $5$ nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are _______. (Neglect the air resistance to the droplets and take $g = 10$ m/s$^2$)

A wire of uniform resistance $\lambda \Omega / \mathrm{m}$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points $A$ and $B(A O B)$ as shown in figure. The equivalent resistance between points $A$ and $B$ is $\_\_\_\_$ $\Omega$. 

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $\mu=2 \mu_{0}$, is ($\mu_{0}=$ permeability of vacuum)

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3$ cm, and of the outermost turn $r_2 = 6$ cm. If $20$ mA current flows in it then the magnetic moment will be $\alpha \times 10^{-2}$ A.m$^2$. The value of $\alpha$ is _____.

The charge stored by the capacitor $C$ in the given circuit in the steady state is $\_\_\_\_$ $\mu \mathrm{C}$. 

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\dfrac{B_1}{B_2}$ is _______. 

Two resistors of $100 \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400 \Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is $\_\_\_\_$ V.

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $2 \Omega$ and $3 \Omega$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance $l \mathrm{~cm}$ from the left. Now when an unknown resistance $x \Omega$ is connected in parallel to $3 \Omega$ resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance $x$ is $\_\_\_\_$ $\Omega$.

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left(\dfrac{v_0}{\sqrt{2}}\hat{x} + \dfrac{v_0}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B} = B_0 \hat{z}$ and a space varying electric field $\vec{E} = E_0 e^{-\lambda x}\hat{x}$ within the region $0 \leq x \leq L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is _______.

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2 A. The magnetic field at its centroid is $\alpha \times 10^{-5} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$. (Given : $\mu_{\mathrm{o}}=4 \pi \times 10^{-7}$ SI units)

An infinitely long straight wire carrying current $I$ is bent in a planer shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is : 

Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as shown in figure. The net electric field at the center of the circle is $\_\_\_\_$. ($\epsilon_{0}$ is permittivity of free space) 

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10 \sin (\omega \mathrm{t}) \mathrm{A}$, where $\omega=1000 \mathrm{rad}. / \mathrm{s}$. A circular conducting loop $(B)$ of radius 1 cm coaxially slided through the solenoid at a speed $v=1 \mathrm{~cm} / \mathrm{s}$. The r.m.s. current through the loop when the coil $B$ is inserted 10 cm inside the solenoid is $\alpha / \sqrt{2} \mu \mathrm{~A}$. The value of $\alpha$ is $\_\_\_\_$. [Resistance of the loop $=10 \Omega$ ]

When an external resistance of $5\ \Omega$ is connected across terminals of a cell, a current of $0.25\text{ A}$ flows through it. When the $5\ \Omega$ resistor is replaced by a $2\ \Omega$ resistor, a current of $0.5\text{ A}$ flows through it. The internal resistance of the cell is _______ $\Omega$.

Two charged conducting spheres $S_1$ and $S_2$ of radii $8$ cm and $18$ cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\dfrac{E_{S_1}}{E_{S_2}}$ is _______.

A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when :

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 _______.

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 $\_\_\_\_$ .

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 _______.

Which one of the following is not a measurable quantity?

The figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference $(\phi)$ between the current and source voltage is $30°$ and phase difference is $60°$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is _______ H. 

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If $P$ is the point where the galvanometer shows zero reading then the length $A P$ is $\_\_\_\_$ cm. 

The equation of the electric field of an electromagnetic wave propagating through free space is given by : $E=\sqrt{377} \sin \left(6.27 \times 10^{3} t-2.09 \times 10^{-5} x\right) \mathrm{N} / \mathrm{C}$ The average power of the electromagnetic wave is $\left(\frac{1}{\alpha}\right) \mathrm{W} / \mathrm{m}^{2}$. The value of $\alpha$ is $\_\_\_\_$ (Take $\sqrt{\frac{\mu_{0}}{\varepsilon_{o}}}=377$ in SI units)

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