Electromagnetism PYQ — Page 37

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$ 

The magnetic field in a region is given by $\vec{B}={B}_{0}(\frac{x}{a})\hat{k}$. A square loop of side d is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec{v}={v}_{0}\hat{i}$. The emf induced in the loop is : 

If you are provided a set of resistances, $2\Omega ,4\Omega ,6\Omega$ and $8\Omega .$ Connect these resistances to obtain an equivalent resistance of $\frac{46}{3}\Omega$.

Consider the combination of two capacitors ${C}_{1}$ and ${C}_{2}$, with ${C}_{2}>{C}_{1}$, when connected in parallel, the equivalent capacitance is $10$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{{C}_{2}}{{C}_{1}}$.

A series LCR circuit of $R=5\Omega ,L=20\mathrm{mH}$ and $C=0.5\mu F$ is connected across an $\mathrm{AC}$ supply of $250V,$ having variable frequency. The power dissipated at resonance condition is ________$\times {10}^{2}W.$

Two ideal electric dipoles $A$ and $B$, having their dipole moment ${p}_{1}$ and ${p}_{2}$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$, the resultant electric field is making an angle of $37^{\circ}$ with the axis. The ratio of the dipole moment of $A$ and $B,\frac{{p}_{1}}{{p}_{2}}$ is$:($ take $\mathrm{sin}37^{\circ}=\frac{3}{5})$ 

Two capacitors of capacities $2C$ and $C$ are joined in parallel and charged up to potential $V.$ The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K.$ The potential difference across the capacitors will now be:

The material filled between the plates of a parallel plate capacitor has resistivity $200\Omega m$. The value of capacitance of the capacitor is $2\mathrm{pF}$. If a potential difference of $40V$ is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is $50$)

A square-shaped wire with a resistance of each side $3\Omega$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in a unit of $\Omega$ will is, _____.

An $AC$ current is given by $I={I}_{1}sin\omega t+{I}_{2}cos\omega t.$ A hot wire ammeter will give a reading:

In a scries $LCR$ resonance circuit, if we change the resistance only, from a lower to higher value :

A $100\Omega$ resistance, a $0.1\mu F$ capacitor and an inductor are connected in series across a $250V$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60\mathrm{Hz}$.

The peak electric field produced by the radiation coming from the $8W$ bulb at a distance of $10m$ is $\frac{x}{10}\sqrt{\frac{{\mu }_{0}c}{\pi }}V{m}^{-1}$. The efficiency of the bulb is $10%$ and it is a point source. The value of $x$ is,

The alternating current is given by, $i={\sqrt{42}\mathrm{sin}(\frac{2\pi }{T}t)+10}A$. The R.M.S. value of this current is __________ $A$.

Calculate the amount of charge on capacitor of $4\mu F.$ The internal resistance of battery is $1\Omega :$ 

There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is $1:1$. The magnetic field at point $P$ is$_________.$ 

A certain charge $Q$ is divided into two parts $q$ and $(Q-q).$ How should the charges $Q$ and $q$ be divided so that $q$ and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?

In a parallel plate capacitor set up, the plate area of capacitor is $2{m}^{2}$ and the plates are separated by $1m$. If the space between the plates are filled with a dielectric material of thickness $0.5m$ and are $2{m}^{2}$ (see figure) the capacitance of the set-up will be ${\epsilon }_{0}$ ________. (Dielectric constant of the material $=3.2$) (Round off to the Nearest Integer) 

A steel rod with $y=2.0\times {10}^{11}N{m}^{-2}$ and $\alpha ={10}^{-5}{C\circ }^{-1}$ of length $4m$ and area of cross-section $10{\mathrm{cm}}^{2}$ is heated from $0^{\circ}C$ to $400^{\circ}C$ without being allowed to extend. The tension produced in the rod is $x\times {10}^{5}N$ where the value of $x$ is $_________.$

A series LCR circuit driven by $300V$ at a frequency of $50\mathrm{Hz}$ contains a resistance $R=3k\Omega$, an inductor of inductive reactance ${X}_{L}=250\pi \Omega$ and an unknown capacitor. The value of capacitance to maximise the average power should be: $(\text{take}{\pi }^{2}=10)$

$512$ identical drops of mercury are charged to a potential of $2V$ each. The drops are joined to form a single drop. The potential of this drop is $V$ in Volt.

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 $s$).

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

In an LCR series circuit, the power factor is unity. What is the phase difference between current and voltage?