Electromagnetism PYQ — Page 4

A parallel plate capacitor has capacitance $C$, when there is vacuum within the parallel plates. A sheet having thickness $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is :

A capacitor $P$ with capacitance $10 \times 10^{-6} \mathrm{~F}$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 10^{-6} \mathrm{~F}$. The charge on capacitor $Q$ when equilibrium is established will be $\alpha \times 10^{-5} C$ (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ 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.

Refer to the figure given below, current between terminals $A$ and $B$ is _____ A. 

In the potentiometer, when the cell in the secondary circuit is shunted with $4 \Omega$ resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with $12 \Omega$ resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is $\_\_\_\_$ $\Omega$

The reading of the ammeter $(A)$ in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is $\_\_\_\_$ A. 

The heat generated in 1 minute between points $A$ and $B$ in the given circuit, when a battery of 9 V with internal resistance of $1 \Omega$ is connected across these points is $\_\_\_\_$ J. 

A solenoid has a core made of material with relative permeability $400$. The magnetic field produced in the interior of solenoid is $1.0$ T. The magnetic intensity in SI units is $\alpha \times 10^5$. The value of $\alpha$ is ______. (Free space permeability $\mu_0=4\pi \times 10^{-7}$ SI units.)

Electric field in a region is given by $\vec{E}=A x \hat{i}+B y \hat{j}$, where $A=10 \mathrm{~V} / \mathrm{m}^{2}$ and $B=5 \mathrm{~V} / \mathrm{m}^{2}$. If the electric potential at a point $(10,20)$ is 500 V, then the electric potential at origin is $\_\_\_\_$ V.

Two point charges $2 q$ and $q$ are placed at vertex $A$ and centre of face $C D E F$ of the cube as shown in figure. The electric flux passing through the cube is : 

Two point charges $8 \, \mu C$ and $-2 \, \mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii $3$ cm and $5$ cm with their centers at the origin is _______.

A $5$ mg particle carrying a charge of $5\pi\times 10^{-6}$ C is moving with velocity of $(3\hat{i}+2\hat{k})\times 10^{-2}$ m/s in a region having magnetic field $\vec{B} = 0.1\hat{k}$ Wb/m$^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes $5$ revolutions. The value of $\alpha$ is ________.

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)?

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_0 e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is $\_\_\_\_$. $(\pi=3.14)$

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 $\_\_\_\_$ $\mu \mathrm{F}$. 

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is $2 \Omega$ then the force needed to move the rod towards right with constant speed (v) of $1.5 \mathrm{~m} / \mathrm{s}$ is $\_\_\_\_$ N. 

To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is $\_\_\_\_$.

A parallel plate air capacitor has a capacitance $C$. When it is half filled as show in figure with a dielectric constant $K = 5$, the percentage increase in the capacitance is _______. 

A $30$ cm long solenoid has $10$ turns per cm and area of $5$ cm$^2$. The current through the solenoid coil varies from $2$ A to $4$ A in $3.14$ s. The e.m.f. induced in the coil is $\alpha\times 10^{-5}$ V. The value $\alpha$ is ________.

The equivalent resistance between the points $A$ and $B$ in the following circuit is $\frac{x}{5} \Omega$. The value of $x$ is $\_\_\_\_$. 

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)=25 \sin \left(2.0 \times 10^{15} t-10^{7} x\right) \hat{n}$ then the refractive index of the medium is $\_\_\_\_$. (All given measurement are in SI units)

A moving coil galvanometer of resistance $100 \Omega$ shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is $\_\_\_\_$ $\Omega$

For an electromagnetic wave propagating through vacuum, $\vec{k}$, $\vec{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :