Physics Electromagnetism questions from JEE Main 2012.
A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius $R$, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be
Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires $A$ and $B$ respectively in opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2 \mathrm{~m}$. The force acting on the conductor $B$, which is situated at $10 \mathrm{~cm}$ distance from $A$ will be
The magnetic force acting on charged particle of charge $2 \mu \mathrm{C}$ in magnetic field of $2 T$ acting in $y-$ direction, when the particle velocity is $(2 \hat{i}+3 \hat{j}) \times 10^6 \mathrm{~ms}^{-1}$ is
The velocity of certain ions that pass undeflected through crossed electric field $E=7.7 \mathrm{k} \mathrm{V} / \mathrm{m}$ and magnetic field $B=0.14 \mathrm{~T}$ is
The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $10 \mathrm{~g}$ and is $5 \mathrm{~cm}$ long. The wire is hanging as shown in the figure. The springs stretch $0.5 \mathrm{~cm}$ under the weight of the wire and the circuit has a total resistance of $12 \Omega$. When the lower wire is subjected to a static magnetic field, the springs, stretch an additional $0.3 \mathrm{~cm}$. The magnetic field is 
Magnetic flux through a coil of resistance $10 \Omega$ is changed by $\Delta \phi$ in $0.1 \mathrm{~s}$. The resulting current in the coil varies with time as shown in the figure. Then $|\Delta \phi|$ is equal to (in weber) 
A coil of self inductance $L$ is connected at one end of two rails as shown in figure. A connector of length $l$, mass $m$ can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction $B$ going into the page. At an instant $t=0$ an initial velocity $v_0$ is imparted to it and as a result of that it starts moving along $x$-axis. The displacement of the connector is represented by the figure. 
An electromagnetic wave with frequency $\omega$ and wavelength $\lambda$ travels in the $+y$ direction. Its magnetic field is along $+x$-axis. The vector equation for the associated electric field (of amplitude $E_0$ ) is
The frequency of $X$-rays; $\gamma$-rays and ultraviolet rays are respectively $a, b$ and $c$ then
An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\vec{X}$ and that of wave propagation by $\overrightarrow{\mathrm{k}}$. Then :
Three resistors of $4 \Omega, 6 \Omega$ and $12 \Omega$ are connected in parallel and the combination is connected in series with a $1.5 \mathrm{~V}$ battery of $1 \Omega$ internal resistance. The rate of Joule heating in the $4 \Omega$ resistor is
A resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t=$ 0 . If after $t$ sec the voltage across the capacitance was seven times the voltage across $\mathrm{R}$, the value of $\mathrm{t}$ is
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: Self inductance of a long solenoid of length $L$, total number of turns $\mathrm{N}$ and radius $\mathrm{r}$ is less than $\frac{\pi \mu_0 N^2 r^2}{L}$. Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current $I$ is $\frac{\mu_0 N I}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.
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: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.
A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :
A charge $Q$ is uniformly distributed over the surface of non conducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure
In an $L C R$ circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of $220 \mathrm{~V}$ and $100 \mathrm{~Hz}$ is connected to it as shown? 
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: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is $6.4 \times 10^6 \mathrm{~m}$.
A radio transmitter transmits at $830 \mathrm{kHz}$. At a certain distance from the transmitter magnetic field has amplitude $4.82 \times 10^{-11} \mathrm{~T}$. The electric field and the wavelength are respectively
Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches   Circuit (a) Circuit (b)
Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_\alpha$. Which one of the following relations is correct?
The electric potential $V(x)$ in a region around the origin is given by $V(x)=4 x^2$ volts. The electric charge enclosed in a cube of $1 \mathrm{~m}$ side with its centre at the origin is (in coulomb)
A generator has armature resistance of $0.1 \Omega$ and develops an induced emf of $120 \mathrm{~V}$ when driven at its rated speed. Its terminal voltage when a current of $50 \mathrm{~A}$ is being drawn is
The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric field $\vec{E}$ is applied at an angle $\frac{\pi}{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is 
Three positive charges of equal value $q$ are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in
In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be
A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R(R$ $>r$ ) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
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. An insulating solid sphere of radius $\mathrm{R}$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement $1$: When a charge $q$ is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{\mathrm{qp}}{3 \varepsilon_0}$ Statement $2$: The electric field at a distance $r(r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \varepsilon_0}$
The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is $10 \mathrm{kHz}$. When the container is filled with a gas, the resonance frequency changes by $50 \mathrm{~Hz}$. The dielectric constant of the gas is
A series combination of $n_1$ capacitors, each of capacity $C_1$ is charged by source of potential difference $4 \mathrm{~V}$. When another parallel combination of $n_2$ capacitors each of capacity $C_2$ is charged by a source of potential difference $V$, it has the same total energy stored in it as the first combination has. The value of $C_2$ in terms of $C_1$ is then
The figure shows an experimental plot for discharging of a capacitor in an $R-C$ circuit. The time constant $\tau$ of this circuit lies between: 
In a sensitive meter bridge apparatus the bridge wire should possess
A $6.0$ volt battery is connected to two light bulbs as shown in figure. Light bulb 1 has resistance 3 ohm while light bulb 2 has resistance $6 \mathrm{ohm}$. Battery has negligible internal resistance. Which bulb will glow brighter? 
The resistance of a wire is $R$. It is bent at the middle by $180^{\circ}$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is
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: The possibility of an electric bulb fusing is higher at the time of switching $\mathrm{ON}$. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.
Two electric bulbs marked $25 \mathrm{~W}-220 \mathrm{~V}$ and $100 \mathrm{~W}-220 \mathrm{~V}$ are connected in series to a $440 \mathrm{~V}$ supply. Which of the bulbs will fuse?
A bar magnet of length $6 \mathrm{~cm}$ has a magnetic moment of $4 \mathrm{~J} \mathrm{~T}^{-1}$. Find the strength of magnetic field at a distance of $200 \mathrm{~cm}$ from the centre of the magnet along its equatorial line.