Electromagnetism PYQ — Page 63

A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec{E}=\vec{E}_0\left(4 \times 10^{-7} x-50 t\right)$ with distance being in meter and time in seconds. The dielectric constant of the medium is :

A current $i$ is flowing in a straight conductor of length $L$. The magnetic induction at a point on its axis at a distance $\frac{L}{4}$ from its centre will be :

Six equal resistances are connected between points $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ as shown in figure. Then net resistance will be maximum between : 

A series $\mathrm{LR}$ circuit is connected to an ac source of frequency $\omega$ and the inductive reactance is equal to $2 \mathrm{R}$. A capacitance of capacitive reactance equal to $\mathrm{R}$ is added in series with $\mathrm{L}$ and $\mathrm{R}$. The ratio of the new power factor to the old one is :

Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical. If the mass of each charge is $m$, then the electrostatic potential at the centre of line joining them will be $$ \left(\frac{1}{4 \pi \in_0}=k\right) \text {. } $$

A particle of charge $16 \times 10^{-16} \mathrm{C}$ moving with velocity $10 \mathrm{~ms}^{-1}$ along $x$-axis enters a region where magnetic field of induction $\vec{B}$ is along the $y$-axis and an electric field of magnitude $10^4 \mathrm{Vm}^{-1}$ is along the negative $z$-axis. If the charged particle continues moving along $x$-axis, the magnitude of $\vec{B}$ is :

When resonance is produced in a series LCR circuit, then which of the following is not correct?

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to :

An LCR circuit as shown in the figure is connected to a voltage source $\mathrm{V}_{\mathrm{ac}}$ whose frequency can be varied.  The frequency, at which the voltage across the resistor is maximum, is :

To establish an instantaneous current of $2 \mathrm{~A}$ through a $1 \mu \mathrm{F}$ capacitor ; the potential difference across the capacitor plates should be changed at the rate of:

A parallel plate capacitor of area $60 \mathrm{~cm}^2$ and separation $3 \mathrm{~mm}$ is charged initially to $90 \mu \mathrm{C}$. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5 \times 10^{-8} \mathrm{C} / \mathrm{s}$, then what is the magnetic field between the plates ?

A shunt of resistance $1 ~\Omega$ is connected across a galvanometer of $120 ~\Omega$ resistance. A current of $5.5$ ampere gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly :

This question has $Statement I$ and $Statement II$. Of the four choices given after the Statements, choose the one that best describes the two Statements. $Statement - I :$ Higher the range, greater is the resistance of ammeter. $Statement - II :$ To increase the range of ammeter, additional shunt needs to be used across it.

Which of the four resistances $P, Q, R$ and $S$ generate the greatest amount of heat when a current flows from A to B ? 

A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of $25.5$ $\mathrm{kVm}^{-1}$. The density of liquid is $1.26 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$. The radius of the drop is (neglect buoyancy).

The gravitational field in a region is given by: $\vec{E}=(5 N / k g) \hat{i}+(12 N / k g) \hat{j}$ If the potential at the origin is taken to be zero, then the ratio of the potential at the points $(12 \mathrm{~m}, 0)$ and $(0,5 \mathrm{~m})$ is :

The surface charge density of a thin charged disc of radius $\mathrm{R}$ is $\sigma$. The value of the electric field at the centre of the disc is $\frac{\sigma}{2 \in_0}$. With respect to the field at the centre, the electric field along the axis at a distance $\mathrm{R}$ from the centre of the disc:

A dc source of emf $\mathrm{E}_1=100 \mathrm{~V}$ and internal resistance $r=0.5 \Omega$, a storage battery of emf $\mathrm{E}_2=90 \mathrm{~V}$ and an external resistance $\mathrm{R}$ are connected as shown in figure. For what value of R no current will pass through the battery? 

In the circuit shown here, the voltage across $\mathrm{E}$ and $\mathrm{C}$ are respectively $300 \mathrm{~V}$ and $400 \mathrm{~V}$. The voltage $\mathrm{E}$ of the ac source is : 

A uniform electric field $\vec{E}$ exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to $\vec{E}$. The path of the particle between the plates is a:

A rectangular loop of wire, supporting a mass $m$, hangs with one end in a uniform magnetic field $\vec{B}$ pointing out of the plane of the paper. A clockwise current is set up such that $i>m g / B a$, where $a$ is the width of the loop. Then : 

A letter ${ }^{\prime} \mathrm{A}^{\prime}$ is constructed of a uniform wire with resistance $1.0 \Omega$ per $\mathrm{cm}$, The sides of the letter are $20 \mathrm{~cm}$ and the cross piece in the middle is $10 \mathrm{~cm}$ long. The apex angle is 60 . The resistance between the ends of the legs is close to:

Two short bar magnets of length $1cm$ each have magnetic moments $1.20A{m}^{2}$ and $1.00A{m}^{2}$ respectively. They are placed on a horizontal table parallel to each other with their $\text{N}$ poles pointing towards the south. They have a common magnetic equator and are separated by a distance of $20.0\mathrm{cm}$. The value of the resultant horizontal magnetic induction at the mid-point $\text{O}$ of the line joining their centres is close to ( Horizontal component of earth's magnetic induction is $3.6\times {10}^{-5}\mathrm{Wb}{m}^{-2}$ )

A point charge of magnitude $+1 \mu \mathrm{C}$ is fixed at $(0$, $0,0)$. An isolated uncharged spherical conductor, is fixed with its center at $(4,0,0)$. The potential and the induced electric field at the centre of the sphere is :