JEE Main 2016 — Electromagnetism

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\rho =\frac{A}{r}$ , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is: 

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ going into the plane of the paper (see figure). If charge densities ${\sigma }_{1}$ and ${\sigma }_{2}$ are induced on the left and right surfaces respectively of the sheet, then (ignore fringe effects) 

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

Two identical wires $A$ and $B$, each of length $l$, carry the same current $I$ . Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $a$. If ${B}_{A}$ and ${B}_{B}$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{{B}_{A}}{{B}_{B}}$ is

 In the circuit shown, the resistance r is a variable resistance. If for $r=fR$ , the heat generation in r is maximum then the value of $f$ is

Microwave oven acts on the principle of:

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when $R.B.=2400 \Omega .$Deflection becomes 20 divisions when resistance taken from resistance box is 4900 Ω. Then we can conclude :  Note: This question is awarded as the bonus. Now the question is corrected.

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of ${75}^{o}$. One of the fields has a magnitude of $15\mathrm{mT}$. The dipole attains stable equilibrium at an angle of ${30}^{o}$ with this field. The magnitude of the other field (in $\mathrm{mT}$) is close to

A galvanometer having a coil resistance of $100 \Omega$ gives a full scale deflection, when a current of $1\mathrm{mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10A$, is:

To know the resistance $G$ of a galvanometer by half deflection method, a battery of emf ${V}_{E}$ and resistance $R$ is used to deflect the galvanometer by angle $\theta$ . If a shunt of resistance $S$ is needed to get half deflection the $G$, $R$ and $S$ are related by the equation:

The resistance of an electrical toaster has a temperature dependence given by $R(T)={R}_{0}[1+\alpha (T-{T}_{0})]$ in its range of operation. At ${T}_{0}=300 K, R=100\Omega \text{and} at T=500 K, R=120 \Omega$. The toaster is connected to a voltage source at $200V$ and its temperature is raised at a constant rate from $300\text{to}500K$ in $30s$. The total work done in raising the temperature is : Note: This question was awarded as the bonus since all options were incorrect in the exam.

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement:

Arrange the following electromagnetic radiations per quantum in the order of increasing energy: $A:$ Blue light $B:$ Yellow light $C:$ X-ray $D:$ Radiowave

Three capacitors each of $4 \mu F$ are to be connected in such a way that the effective capacitance is $6 \mu F$. This can be done by connecting them

A series $LR$ circuit is connected to a voltage source with $V(t)={V}_{0}\mathrm{sin}(\omega t)$ . After a very large time, current $I(t)$ behaves as $({t}_{0}\gg \frac{L}{R})$:

A $50 \Omega$ resistance is connected to a battery of $5V$. A galvanometer of resistance $100 \Omega$ is to be used as an ammeter to measure current through the resistance, for this a resistance ${r}_{S}$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is with in $1%$ of the current without the ammeter in the circuit?

A conducting metal circular-wire-loop of radius $r$ is placed perpendicular to a magnetic field which varies with time as $B={B}_{0}{e}^{-\frac{t}{\tau }},$ where ${B}_{0} \mathrm{and} \tau$ are constants at time $t=0$. If the resistance of the loop is $R$, then the heat generated in the loop after a long time $(t\rightarrow \infty )$ is

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4 \mu F$ and $9 \mu F$ capacitors), at a point distant 30 m from it, would equal: 

Within a spherical charge distribution of charge density $\rho (r),$ N equipotential surfaces of potential ${V}_{0}, {V}_{0}+\Delta V, {V}_{0}+2\Delta V,\ldots {V}_{0}+N\Delta V (\Delta V>0),$ are drawn and have increasing radii ${r}_{0}, {r}_{1}, {r}_{2},\ldots {r}_{N},$ respectively. If the difference in the radii of the surfaces is constant for all values of ${V}_{0} and \Delta V$ then :

Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be $1 \mu F$ is : 

The potential (in volts) of a charge distribution is given by $V(z)=30-5{z}^{2}$ for $|z|\leq 1 m$ $V(z)=35-10 |z|$ for $|z|\geq 1 m$ . $V(z)$ does not depend on x and y. If this potential is generated by a constant charge per unit volume ${\rho }_{0}$ (in units of ${\epsilon }_{0}$ ) which is spread over a certain region, then choose the correct statement.