Electromagnetism PYQ — Page 51

A parallel plate capacitor is made of two square plates of side $a,$ separated by a distance $d (d\ll a).$ The lower triangular portion filled with a dielectric of dielectric constant $K,$ as shown in the figure. Capacitance of this capacitor is: 

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is $E=6 V {m}^{-1}$ along y-direction. Its corresponding magnetic field component, $B$ would be:

Drift speed of electrons, when $1.5 A$ current flows in a copper wire of cross section $5 {\mathrm{mm}}^{2}$ is ${v}_{d}.$ If the electron density in copper is $9\times {10}^{28}{m}^{-3}$ the value of ${v}_{d}$ in $\mathrm{mm}{s}^{-1}$ is close to (Take charge of an electron to be $=1.6\times {10}^{-19} C$)

A thin strip $10 cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5 N {m}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of $0.1 T.$ If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$ . If the mass of the strip is $50$ grams, its resistance $10\Omega$ and air drag negligible, $N$ will be close to: 

The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as ${R}_{1}$ has the colour code (orange, red, brown). The resistors ${R}_{2}$ and ${R}_{4}$ are $80\Omega$ and $40\Omega$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as ${R}_{3}$, would be 

The magnetic field of an electromagnetic wave is given by: $\vec{B}=1.6\times {10}^{-6}\mathrm{cos}⁡ (2\times {10}^{7}z+6\times {10}^{15}t) (2\hat{i}+\hat{j})\frac{Wb}{{m}^{2}}$ The associated electric field will be:

A $20$ $\text{H}$ inductor coil is connected to a $10$ $\Omega$ resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is: 

Determine the charge on the capacitor in the following circuit: 

In free space, a particle $A$ of charge $1 \mu C$ is held fixed at point $P$ . Another particle $B$ of the same charge and mass $4 \mu g$ is kept at a distance of $1 mm$ from $P.$ If $B$ is released, then its velocity at a distance of $9 mm$ from $P$ is: [Take $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9} N {m}^{2} {C}^{-2}$ ]

The figure shows a capacitor of capacitance $C$ connected to a battery via a switch, having a total charge $Q$ on it, in steady-state. When the switch $S$ is turned from position $A$ to position $B$, the energy dissipated in the circuit is 

A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is: ( $E$ is mid-point of arm $CD$ ) 

In the figure shown below, the charge on the left plate of the 10F capacitor is -30C. The charge on the right plate of the 6F capacitor is: 

The actual value of resistance $R$ , shown in the figure is $30\Omega .$ This is measured in an experiment as shown using the standard formula $R=\frac{V}{I}$ , where $V$ and $I$ are the readings of the voltmeter and ammeter, respectively. If the measured value of $R$ is $5%$ less, then the internal resistance of the voltmeter is: 

A coil of self inductance $10 mH$ and resistance of $0.1 \Omega$ is connected through a switch to a battery of internal resistance $0.9 \Omega$ . After the switch is closed, the time taken for the current to attain $80%$ of the saturation value is: $[ \mathrm{ln}5=1.6 ]$

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line.  One may conclude that

Three charges $+Q, q,+Q$ are placed respectively, at distance, $0,d/2$ and $d$ from the origin, on the $x$ -axis. If the net force experienced by $+Q,$ placed at $x=0,$ is zero, then value of $q$ is:

The resistance of a galvanometer is $50 ohm$ and the maximum current which can be passed through it is $0.002 A.$ What resistance must be connected to it in order to convert it into an ammeter of range $0-0.5 A?$

The electric field in a region is given by $\vec{E}=(Ax+B) \hat{i} ,$ where $E$ is in $N{C}^{-1}$ and $x$ is in metres. The values of constants are $A=20 SI$ unit and $B=10 SI$ unit. If the potential at $x=1$ is ${V}_{1}$ and that at $x=-5$ is ${V}_{2},$ then ${V}_{1}-{V}_{2}$ is

A simple pendulum of length $L$ is placed between the plates of a parallel plate capacitor having electric field $E$ , as shown in figure. Its bob has mass $m$ and charge $q$ . The time period of the pendulum is given by: 

A particle having the same charge as of electron moves in a circular path of radius $0.5 cm$ under the influence of a magnetic field of $0.5 T.$ If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $=1.6\times {10}^{-19}C$ )

The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V.$ When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed the two plates of the first capacitor. The new potential difference of the combined system is:

A rigid square loop of side $‘a’$ and carrying current ${I}_{2}$ is lying on a horizontal surface near a long current ${I}_{1}$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be: 

Let a total charge $2Q$ be distributed in a sphere of radius $R,$ with the charge density given by $\rho (r)=kr,$ where $r$ is the distance from the centre. Two charges $A$ and $B$ , of $-Q$ each, are placed on diametrically opposite points, at equal distance, a, from the centre. If $A$ and $B$ do not experience any force, then:

A galvanometer having a resistance of $20 \Omega$ and 30 division on both sides has figure of merit 0.005 ampere/ division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is: