JEE Main 2013 — Electromagnetism

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is : 

A circular loop of radius $0.3\mathrm{cm}$ lies parallel to a much bigger circular loop of radius $20\mathrm{cm}$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is$15$ $\mathrm{cm}$. If a current of $2.0A$ flows through the smaller loop, then the flux linked with a bigger loop 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 :

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? 

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:

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).

A metal sample carrying a current along $\mathrm{X-}$ axis with density $\mathrm{J}_{\mathrm{x}}$ is subjected to a magnetic field $\mathrm{B}_z$ (along $\mathrm{z-}$axis). The electric field $\mathrm{E}_{\mathrm{y}}$ developed along $\mathrm{Y}$-axis is directly proportional to $\mathrm{J}_{\mathrm{x}}$ as well as $\mathrm{B}_{\mathrm{z}}$. The constant of proportionality has SI unit.

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is: 

A parallel plate capacitor having a separation between the plates $\mathrm{d}$, plate area $\mathrm{A}$ and material with dielectric constant $\mathrm{K}$ has capacitance $\mathrm{C}_0$. Now one-third of the material is replaced by another material with dielectric constant $2 \mathrm{~K}$, so that effectively there are two capacitors one with area $\frac{1}{3} \mathrm{~A}$, dielectric constant $2 \mathrm{~K}$ and another with area $\frac{2}{3} \mathrm{~A}$ and dielectric constant $\mathrm{K}$. If the capacitance of this new capacitor is $\mathrm{C}$ then $\frac{\mathrm{C}}{\mathrm{C}_0}$ is

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 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 :

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 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 :

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 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 :

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 :

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:

An electric current is flowing through a circular coil of radius $\mathrm{R}$. The ratio of the magnetic field at the centre of the coil and that at a distance $2 \sqrt{2} R$ from the centre of the coil and on its axis is :

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 :

Choose the correct sketch of the magnetic field lines of a circular current loop shown by the dot $$ \text { and the cross } \otimes \text {. } $$

Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential :

In a metre bridge experiment null point is obtained at $40 \mathrm{~cm}$ from one end of the wire when resistance $\mathrm{X}$ is balanced against another resistance $\mathrm{Y}$. If $\mathrm{X} < \mathrm{Y}$, then the new position of the null point from the same end, if one decides to balance a resistance of $3 \mathrm{X}$ against $\mathrm{Y}$, will be close to :

In a series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit, $\mathrm{C}=10^{-11}$ Farad, $\mathrm{L}=10^{-}$ ${ }^5$ Henry and $\mathrm{R}=100 \mathrm{Ohm}$, when a constant D.C. voltage $\mathrm{E}$ is applied to the circuit, the capacitor acquires a charge $10^{-9}$ C. The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage $\mathrm{E}_0$ is equal to the constant D.C. voltage E. At resonance the peak value of the charge acquired by the capacitor will be :

In an $\text{LCR}$ circuit as shown below both switches are open initially. Now switch ${\text{S}}_{1}$ is closed, ${\text{S}}_{2}$ kept open. ($\text{q}$ is charge on the capacitor and $\tau = \text{RC}$ is capacitive time constant). Which of the following statement is correct? 

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 : 

One of the two small circular coils, (none of them having any self - inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a dc supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?

Photons of an electromagnetic radiation has an energy $11 \mathrm{keV}$ each. To which region of electromagnetic spectrum does it belong ?

Select the correct statement from the following :

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 : 

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals :

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 magnetic field in a travelling electromagnetic wave has a peak value of $20nT$. The peak value of electric field strength is :

The supply voltage to a room is $120V$. The resistance of the lead wires is $6 \Omega$. A $60W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240W$ heater is switched on in parallel to the bulb?

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:

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.

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: No work is required to be done to move a test charge between any two points on an equipotential surface. Statement 2 : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other.

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:

To find the resistance of a galvanometer by the half deflection method the following circuit is used with resistances $\mathrm{R}_1=9970 \mathrm{~W}, \mathrm{R}_2=30 \mathrm{~W}$ and $\mathrm{R}_3=0$. The deflection in the galvanometer is d. With $\mathrm{R}_3=107 \mathrm{~W}$ the deflection changed to $\frac{d}{2}$. The galvanometer resistance is approximately: 

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 :

Two capacitors ${C}_{1}$ and ${C}_{2}$ are charged to $\text{120 V}$ and $\text{200 V}$ respectively. It is found that by connecting them together the potential on each one can be made zero. Then:

Two coils, $\mathrm{X}$ and $\mathrm{Y}$, are kept in close vicinity of each other. When a varying current, $I(t)$, flows through coil $\mathrm{X}$, the induced $\operatorname{emf}(V(t))$ in coil $\mathrm{Y}$, varies in the manner shown here. The variation of $I(t)$, with time, can then be represented by the graph labelled as graph :  (A) (B) (C) (D)

Two point dipoles of dipole moment $\vec{p}_1$ and $\vec{p}_2$ are at a distance $x$ from each other and $\vec{p}_1 || \vec{p}_2$. The force between the dipoles is :

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 $3.6\times {10}^{-5}\mathrm{Wb}{m}^{-2}$ )

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 $$ \left(\frac{1}{4 \pi \in_0}=k\right) \text {. } $$

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

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