Electromagnetism Questions

In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. ($q$ is charge on the capacitor and $\tau =RC$ is capacitive time constant). Which of the following statement is correct?

A diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250\text{pF}$ in parallel with a load resistance $100\text{k}\Omega$. Find the maximum modulated frequency which could be detected by it.

The supply voltage to a room is $120\text{V}$. The resistance of the lead wires is $6\Omega$. A $60\text{W}$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240\text{W}$ heater is switched on in parallel to the bulb?

Two charges, each equal to $q$, are kept at $x=-a$ and $x=a$ on the $x$ -axis. A particle of mass $m$ and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $y$ ($y\ll a$) along the $y$ -axis, the net force acting on the particle is proportional to:

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the e.m.f. induced across the ends of the rod is:

Statement- I: Higher the range, greater is the resistance of ammeter.Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

Two capacitors $C_1$ and $C_2$ are charged to $120\text{V}$ and $200\text{V}$ respectively. It is found that by connecting them together the potential on each one can be made zero. Then:

A circular loop of radius $0.3\text{cm}$ lies parallel to a much bigger circular loop of radius $20\text{cm}$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15\text{cm}$. If a current of $2.0\text{A}$ flows through the smaller loop, then the flux linked with bigger loop is:

A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ (where $O,A,B$ are collinear) is:

The $I-V$ characteristic of an LED is:

The magnetic field in a travelling electromagnetic wave has a peak value of $20\text{nT}$. The peak value of electric field strength is:

Two short bar magnets of length $1\text{cm}$ each have magnetic moments $1.20{\text{Am}}^2$ and $1.00{\text{Am}}^2$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0\text{cm}$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to ($B_H=3.6\times 10^{-5}{\text{Wb/m}}^2$):