JEE Main 2011 — Electromagnetism

A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \mathrm{NA}^{-1} \mathrm{~m}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2 \mathrm{~m}$ long. If the speed of the boat is $1.50 \mathrm{~ms}^{-1}$, the magnitude of the induced emf in the wire of aerial is :

A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius $\mathrm{R}$. The magnitude of the magnetic induction along its axis is

A fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is :

A resistor 'R' and $2 \mu \mathrm{F}$ capacitor in series is connected through a switch to $200 \mathrm{~V}$ direct supply. Across the capacitor is a neon bulb that lights up at $120 \mathrm{~V}$. Calculate the value of $R$ to make the bulb light up $5 \mathrm{~s}$ after the switch has been closed. $\left(\log _{10} 2.5=0.4\right)$

The electrostatic potential inside a charged spherical ball is given by $\phi=\alpha \rho^2+b$ where $r$ is the distance from the centre; $a, b$ are constants. Then the charge density inside ball is

Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance $d(d< < 1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,