JEE Main 2017 — Electromagnetism

A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I={I}_{0}\mathrm{cos}⁡(\omega t).$ The emf induced in the smaller inner loop is nearly:

A sinusoidal voltage of peak value $283V$ and angular frequency $320{s}^{-1}$ is applied to a series $LCR$ circuit. Given that $R=5 \Omega , L=25 \mathrm{mH}$ and $C=1000\mu F$. The total impedance and phase difference between the voltage across the source and the current will respectively be-

The electric field component of a monochromatic radiation is given by $\vec{E}=2{E}_{0}\mathrm{cos}kz\mathrm{cos}\omega t\hat{i}$, Its magnetic field $\vec{B}$ is then given by:

A uniform magnetic field $B$ of $0.3T$ is along the positive $\text{Z}$ -direction. A rectangular loop ($abcd$) of sides $10 \mathrm{cm}\times 5 \mathrm{cm}$ carries a current $I$ of $12A$. Out of the following different orientations which one corresponds to stable equilibrium?

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $X-$rays. It produces continuous as well as characteristic $X-$rays. If ${\lambda }_{min}$ is the smallest possible wavelength of $X-$ray in the spectrum, the variation of $\mathrm{log}({\lambda }_{min})$ with $\mathrm{log}(V)$ is correctly represented in :

A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

Four closed surfaces and corresponding charge distributions are shown below.  Let the respective electric fluxes through the surfaces be ${\phi }_{1}, {\phi }_{2}, {\phi }_{3}$ and ${\phi }_{4}$. Then:

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between the limits $589.0V$ to $589.8V$. What is the potential at a point on the sphere whose radius vector makes an angle of $60^{\circ}$ with the direction of the field?

In the given circuit diagram, when the current reaches a steady-state in the circuit, the charge on the capacitor of capacitance $C$ will be: 

A capacitance of $2 \mu F$ is required in an electrical circuit across a potential difference of $1\text{.}0\mathrm{kV}$. A large number of $1 \mu F$ capacitors are available which can withstand a potential difference of not more than $300V$. The minimum number of capacitors required to achieve this is:

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec{B}={B}_{0}(\hat{i}+2\hat{j}-4\hat{k})$. If a test charge moving with a velocity $\vec{v}={v}_{0}(3\hat{i}-\hat{j}+2\hat{k})$ experiences no force in that region, then the electric field in the region, in SI units, is:

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:

Magnetic field in a plane electromagnetic wave is given by, $\vec{B}={B}_{0}\mathrm{sin}(kx+\omega t)\hat{j} T$. Expression for corresponding electric field will be: (Where $c$ is speed of light)

 In the above circuit the current in each resistance is:

The energy stored in the electric field produced by a metal sphere is $4.5J$. If the sphere contains $4\mu C$ charge, its radius will be: $[Take:\frac{1}{4\pi {\in }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}]$

An electric dipole has fixed dipole moment $\vec{p}$, which makes angle $\theta$ with respect to $x-$axis. When subjected to an electric field ${\vec{E}}_{1}=E\hat{i},$ it experiences a torque ${\vec{T}}_{1}=\tau \hat{k}$. When subjected to another electric field ${\vec{E}}_{2}= \sqrt{3} {E}_{1}\hat{j}$ it experiences a torque ${\vec{T}}_{2}=-{\vec{T}}_{1}$ . The angle $\theta$ is:

The figure shows three circuits $I, II$ and $III$ which are connected to a $3V$ battery. If the powers dissipated by the configurations $I, II$ and $III$ are ${P}_{1}, {P}_{2}$ and ${P}_{3}$ respectively, then - 

 A $9V$ battery with an internal resistance of $0.5 \Omega$ is connected across an infinite network, as shown in the figure. All ammeters ${A}_{1}, {A}_{2}, {A}_{3}$ and voltmeter $V$ are ideal. Choose the correct statement.

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P=4 \Omega$ and the neutral point $N$ is at $60\mathrm{cm}$ from $A$ . Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80\mathrm{cm}$ from $A$ . The value of unknown resistance $R$ is - 

A combination of parallel plate capacitors is maintained at a certain potential difference.  When a $3\mathrm{mm}$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4\mathrm{mm}$. Find the dielectric constant of the slab.

In a coil of resistance $100\Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: 

A uniform wire of length $l$ and radius $r$ has a resistance of $100 \text{Ω}$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of new wire will be-

A magnetic needle of magnetic moment $6.7\times {10}^{-2} A{m}^{2}$ and moment of inertia $7.5\times {10}^{-6}\mathrm{kg} {m}^{2}$ is performing simple harmonic oscillations in a magnetic field of $0.01T$. Time taken for $10$ complete oscillations is:

When a current of $5\mathrm{mA}$ is passed through a galvanometer having a coil of resistance $15\Omega$, it shows full-scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0-10V$ is:

Which of the following statements is false?