JEE Main 2006 — Electromagnetism

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

The current $\mathrm{I}$ drawn from the 5 volt source will be 

The flux linked with a coil at any instant ' $t$ ' is given by $\phi=10 t^2-50 t+250$ The induced emf at $t=3 \mathrm{~s}$ is

In a Wheatstone's bridge, there resistances $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ connected in the three arms and the fourth arm is formed by two resistances $\mathrm{S}_1$ and $\mathrm{S}_2$ connected in parallel. The condition for bridge to be balanced will be

The Kirchhoff's first law $\left(\sum i=0\right)$ and second law $\left(\sum i R=\sum E\right)$, where the symbols have their usual meanings, are respectively based on

The rms value of the electric field of the light coming from the Sun is $720 \mathrm{~N} / \mathrm{C}$. The average total energy density of the electromagnetic wave is

In a series resonant LCR circuit, the voltage across $R$ is 100 volts and $R=1 \mathrm{k} \Omega$ with $C=2 \mu \mathrm{F}$. The resonant frequency $\omega$ is $200 \mathrm{rad} / \mathrm{s}$. At resonance the voltage across $L$ is

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2-V_1=20 \mathrm{~V}$. (i.e. plate 2 is at a higher potential). The plates are separated by $d=0.1 \mathrm{~m}$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1 . What is its speed when it hits plate $2 ?$ $\left(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}, \mathrm{m}_{\mathrm{e}}=9.11 \times 10^{-31} \mathrm{~kg}\right)$ 

A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold then, an electric current will

The resistance of a bulb filament is $100 \Omega$ at a temperature of $100^{\circ} \mathrm{C}$. If its temperature coefficient of resistance be $0.005$ per ${ }^{\circ} \mathrm{C}$, its resistance will become $200 \Omega$ at a temperature of

A material ' $B$ ' has twice the specific resistance of ' $A$ '. A circular wire made of ' $B$ ' has twice the diameter of a wire made of ' $A$ '. Then for the two wires to have the same resistance, the ratio $\ell_A / \ell_B$ of their respective lengths must be

An inductor $(L=100 \mathrm{mH})$, a resistor $(R=100 \Omega)$ and a battery $(E=100 \mathrm{~V})$ are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points $A$ and $B$. The current in the circuit $1 \mathrm{~mm}$ after the circuit is 

In an $\mathrm{AC}$ generator, a coil with $\mathrm{N}$ turns, all of the same area $\mathrm{A}$ and total resistance $\mathrm{R}$, rotates with frequency $\omega$ in a magnetic field $B$. The maximum value of emf generated in the coil is "

A long solenoid has 200 turns per $\mathrm{cm}$ and carries a current $\mathrm{i}$. The magnetic field at its centre is $6.28 \times 10^{-2}$ Weber $/ \mathrm{m}^2$. Another long solenoid has 100 turns per $\mathrm{cm}$ and it carries a current $\mathrm{i} / 3$. The value of the magnetic field at its centre is

Needles $\mathrm{N}_1, \mathrm{~N}_2$ and $\mathrm{N}_3$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

An electric bulb is rated 220 volt $-100$ watt. The power consumed by it when operated on 110 volt will be

A electric dipole is placed at an angle of $30^{\circ}$ to a non-uniform electric field. The dipole will experience

Two spherical conductors $A$ and $B$ of radii $1 \mathrm{~mm}$ and $2 \mathrm{~mm}$ are separated by a distance of $5 \mathrm{~cm}$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is