Electromagnetism PYQ — Page 44

A simple pendulum of mass ' $m$ ', length ' $l$ ' and charge $'+{q}^{'}$ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be 

 The value of current in the $6\Omega$ resistance is:

An inductor of $10\mathrm{mH}$ is connected to a $20V$ battery through a resistor of $10k\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1\mu s$ is $\frac{x}{100}\mathrm{mA}$. Then $x$ is equal to ______ . (Take ${e}^{-1}=0.37$)

A current of $5A$ is passing through a non-linear magnesium wire of cross-section $0.04{m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (resistivity of magnesium $\rho =44\times {10}^{-8}\Omega m$)

The fractional change in the magnetic field intensity at a distance $r$ from centre on the axis of current carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r<a$)

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

An electromagnetic wave of frequency $3\mathrm{GHz}$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be _________ $\times {10}^{-2}\mathrm{cm}.$

The electric field in a plane electromagnetic wave is given by, $E=50\mathrm{sin}(500x-10\times {10}^{10}t)V{m}^{-1}$. The velocity of an electromagnetic wave in this medium is: (Given $c=$ the speed of light in vacuum).

Find the peak current and resonant frequency of the following circuit (as shown in figure). 

The current $(i)$ at time $t=0$ and $t=\infty$ respectively for the given circuit is : 

A $2\mu F$ capacitor ${C}_{1}$ is first charged to a potential difference of $10V$ using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor ${C}_{2}$ of $8\mu F$. The charge in ${C}_{2}$ on equilibrium condition is $\mu C$. (Round off to the Nearest Integer) 

An inductor coil stores $64J$ of magnetic field energy and dissipates energy at the rate of $640W$ when a current of $8A$ is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit (in $s$).

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

A Copper $(\mathrm{Cu})$ rod of length $25\mathrm{cm}$ and cross-sectional area $3{\mathrm{mm}}^{2}$ is joined with a similar Aluminium $(\mathrm{Al})$ rod as shown in figure. Find the resistance of the combination between the ends $A$ and $B.$ (Take resistivity of Copper $=1.7\times {10}^{-8}\Omega m$, Resistivity of aluminium $=2.6\times {10}^{-8}\Omega m$) 

A series LCR circuit is designed to resonate at an angular frequency ${\omega }_{0}={10}^{5}\mathrm{rad}{s}^{-1}.$ The circuit draws $16W$ power from $120V$ source at resonance. The value of resistance $R$ in the circuit is ________ $\Omega .$

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with ${X}_{L}=R={X}_{C}.$ Impedance of this circuit is :

In the given figure, a battery of emf $E$ is connected across a conductor $PQ$ of length $l$ and different area of cross-sections having radii ${r}_{1}$ and ${r}_{2}({r}_{2}<{r}_{1}).$  Choose the correct option as one moves from $P$ to $Q$.

A charged particle (mass $m$ and charge $q$) moves along $X$ axis with velocity ${V}_{0}$. When it passes through the origin it enters a region having uniform electric field $\vec{E}=-E\hat{j}$ which extends upto $x=d$. Equation of path of electron in the region $x>d$ is: 

A particle of charge $q$ and mass $m$ is moving with a velocity $-v\hat{i}(v\neq 0)$ towards a large screen placed in the $Y-Z$ plane at distance d. If there is magnetic field $\vec{B}={B}_{0}\hat{k},$ the minimum value of $v$ for which the particle will not hit the screen is :

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side $10\mathrm{cm},50$ turns and carrying current$I$ (Ampere) in units of $\frac{{\mu }_{0}I}{\pi }$ is :

The value of current ${i}_{1}$ flowing from $A$ to $C$ in the circuit diagram is : 

A wire of resistance R is bent to form a complete circle. The resistance between two diametrically opposite points is:

Consider two charged metallic spheres ${S}_{1}$ and ${S}_{2}$ of radii ${R}_{1}$ and ${R}_{2},$ respectively. The electric fields ${E}_{1}$ (on ${S}_{1}$ ) and ${E}_{2}$ (on ${S}_{2}$ ) on their surfaces are such that $\frac{{E}_{1}}{{E}_{2}}=\frac{{R}_{1}}{{R}_{2}}.$ Then the ratio ${V}_{1}$ (on ${S}_{1}$ )$/$${V}_{2}$ (on ${S}_{2}$ ) of the electrostatic potentials on each sphere is:

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns/length and carries a current $I.$ The electron gun shoots an electron along the radius of the solenoid with speed $v.$ If the electron does not hit the surface of the solenoid, maximum possible value of $v$ is (all symbols have their standard meaning):