JEE Main 2015 — Electromagnetism

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:

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:

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: 

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

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 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: 

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:

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?

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: 

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 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: 

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 $25\mathrm{cm}$ 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:

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 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 

 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)

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)

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 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.) 

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: 

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

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:

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.)