JEE Main 2015 — Electromagnetism

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\vec{{F}_{1}}$ be the magnetic force on the inner solenoid due to the outer one and $\vec{{F}_{2}}$ be the magnetic force on the outer solenoid due to the inner one. Then:

In the given circuits $(a)$ and $(b)$, switches ${\text{S}}_{1}$ and ${\text{S}}_{2}$ are closed at $\text{t}=0$ and kept close for a long time. The variation of currents in the two circuits for $\text{t}\geq 0$ are shown in the options. (Figures are schematic and not drawn to scale.) 

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor ${C}^{'}$ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor ${C}^{'}$ , must have been connected in: 

The AC voltage across a resistance can be measured using a:

A red $LED$ emits light at $0.1\mathrm{watt}$ uniformly around it. The amplitude of the electric field of the light at a distance of $1m$ from the diode is:

An inductor $( L=0.03 \text{H} )$ and a resistor $(R=0.15 \text{kΩ})$ are connected in series to a battery of $15 \text{V}$ E.M.F. in a circuit shown below. The key ${K}_{1}$ has been kept closed for a long time. Then at $t=0$, ${K}_{1}$ is opened and key ${K}_{2}$ is closed simultaneously. At $t=1 \text{ms}$ , the current in the circuit will be : $(\text{Take},{e}^{5}\approx 150)$ 

A rectangular loop of sides $10\mathrm{cm}$ and $5\mathrm{cm}$, carrying a current $I$ of $12A$, is placed in different orientations as shown in the figure below. (a)  (b)  (c)  (d)  If there is a uniform magnetic field of $0.3T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(\mathrm{ii})$ unstable equilibrium?

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to ${Q}_{0}$ and then connected to the L and R as shown below:  If a student plots graphs of the square of maximum charge $({Q}_{Max}^{2})$ on the capacitor with time (t) for two different values ${L}_{1}$ and ${L}_{2}({L}_{1}>{L}_{2})$ of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

A uniformly charged solid sphere of radius R has potential ${V}_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3{V}_{0}}{2},\frac{5{V}_{0}}{4},\frac{3{V}_{0}}{4}$ and $\frac{{V}_{0}}{4}$ have radius ${R}_{1}$ , ${R}_{2}, {R}_{3}$ and ${R}_{4}$ respectively. Then Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

In the figure is shown a system of four capacitors connected across a $10V$ battery. The charge that will flow from switch S when it is closed is: 

A wire carrying current $I$ is tied between points $P$ and $Q$ and is in the shape of a circular arc of radius $R$ due to a uniform magnetic field $B$ (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle $2{\theta }_{o}$ at the center of the circle (of which it forms an arch) then the tension in the wire is: 

An electromagnetic wave travelling in the $x-$ direction has frequency of $2\times {10}^{14}Hz$ and electric field amplitude of $27V{m}^{–1}$ oscillates in $Y-$direction. From the options given below, which one describes the magnetic field for this wave?

A $25\mathrm{cm}$ long solenoid has the radius $2\mathrm{cm}$ and $500$ turns. It carries a current of $15A$. If it is equivalent to a magnet of the same size and magnetization $\vec{M} (\frac{Magnetic moment}{volume}),$then $|\vec{M}|$ is:

 In the circuit shown, the current in the $1\Omega$ resistor is:

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If ${\sigma }_{1}$ is the surface charge on the inner surface and ${Q}_{1}$ net charge on it and ${\sigma }_{2}$ the surface charge on the outer surface and ${Q}_{2}$ net charge on it then: 

 Two long currents carrying thin wires, both with current $I$, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle ' $\theta$ ' with the vertical. If wires have a mass $\lambda$ per unit length then the value of $I$ is: ($g=$ gravitational acceleration)

An electric field $\vec{E}=(25 \hat{i}+30 \hat{j})N{C}^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x=2m$, $y=2m$ is:

A wire of length $L=20 cm$ is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges $+Q$ and $-Q$ as shown in the figure. The magnitude of the charge on each half is $|Q|={10}^{3}{\epsilon }_{0}$, where ${\epsilon }_{0}$ is the permittivity of free the space. The net electric field at the centre $O$ is 

A $10 \text{V}$ battery with internal resistance $\text{1} \Omega$ and a $15 \text{V}$ battery with internal resistance $0.6 \Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to: 

In the given circuit, charge ${Q}_{2}$ on the $2\mu F$ capacitor changes as C is varied from $1\mu F$ to $3\mu F$. ${Q}_{2}$ as a function of 'C' is given properly by: (figures are drawn schematically and are not to scale) 

In the electric network shown, when no current flows through the $4 \Omega$ resistor in the arm EB, the potential difference between the points A and D will be: 

For plane electromagnetic waves propagating in the $+z$-direction, which one of the following combinations gives the correct possible direction for $\vec{E}$ and $\vec{B}$ field respectively?

A proton (mass $m$) accelerated by a potential difference $V$ flies through a uniform transverse magnetic field $B$. The field occupies a region of space by width $d$. If $\alpha$ be the angle of deviation of proton from the initial direction of motion (see figure), the value of $\mathrm{sin}⁡\alpha$ will be: 

A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral points are found at a distance of $30\mathrm{cm}$ from the magnet on the East-West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in ${\mathrm{Am}}^{2}$ is close to: (Given $\frac{{\mu }_{0}}{4\pi }={10}^{-7}$ in SI units and ${B}_{H}=$ Horizontal component of earth's magnetic field $=3.6\times {10}^{-5}$ Tesla.)

When the current in a coil changes from $\text{5 A}$ to $\text{2 A}$ in $\text{0}\text{.1 s}$, an average voltage of $\text{50} \text{V}$ is produced. The self-inductance of the coil is

Two long straight parallel wires, carrying (adjustable) currents ${I}_{1}$ and ${I}_{2}$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product ${I}_{1}{I}_{2}$ , would be:

Suppose the drift velocity ${v}_{d}$ in a material varied with the applied electric field E as ${v}_{d }\propto \sqrt{E}$. Then $V-I$ graph for a wire made of such a material is best given by:

A thin disc of radius $b=2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $\sigma$ on it. If the electric field on its axis at a height $\text{h}(\text{h}<<\text{a})$ from its centre is given as $\text{C}\text{h}$ then the value of $C$ is 

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $–\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

When $5V$ potential difference is applied across a wire of length $0.1m$, the drift speed of electrons is $2.5\times {10}^{-4} m{s}^{-1}$ . If the electron density in the wire is $8\times {10}^{28} {m}^{-3}$ , the resistivity of the material is close to: