A long cylindrical shell carries a positive surface charge \(\sigma\) in the upper half and a negative surface charge \(-\sigma\) in the lower half. The electric field lines around the cylinder will look like the figure given in:
(Figures are schematic and not drawn to scale)

1.
2.
3.
4.

The bob of a simple pendulum has mass \(2~\text{g}\) and a charge of \(5.0~\mu \text{C}\). It is at rest in a uniform horizontal electric field of intensity \(2000~\text{V/m}\). At equilibrium, the angle that the pendulum makes with the vertical is: (take \(g = 10~\text{m/s}^2\)${\mathrm{}}^{}$)
1. \( \tan ^{-1}(5.0) \)
2. \( \tan ^{-1}(0.5) \)
3. \( \tan ^{-1}(0.2) \)
4. \( \tan ^{-1}(2.0)\)
 

Four point charges \(-q\), \(+q\), \(+q\) and \(-q\) are placed on \(y\)-axis at \(y=-2d\), \(y=-d\), \(y=+d\), \(y=+2d\), respectively. The magnitude of the electric field \(E\) at a point a the \(x\)-axis at \(x=D\), with \(D>>d\), will behave as:
1. \( E \propto \frac{1}{D} \)
2. \( E \propto \frac{1}{D^3} \)
3. \( E \propto \frac{1}{D^4} \)
4. \( E \propto \frac{1}{D^2}\)

A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E\), as shown in figure. Its bob has mass \(m\) and charge \(q\). The time period of the pendulum is given by:

                      
1. \( 2 \pi \sqrt{\frac{L}{\sqrt{{g}^2-\frac{{q}^2 {E}^2}{~{m}^2}}}} \)
2. \(2\pi\sqrt{\frac{L}{\sqrt{({g}+\frac{qE}{m})}}}\)
3. \(2 \pi \sqrt{\frac{{L}}{\sqrt{{g}-\frac{{qE}}{m}}}} \)
4. \( 2 \pi \sqrt{\frac{{L}}{\sqrt{{g}^2+\left(\frac{{qE}}{{m}}\right)^2}}} \)

Shown in the figure is a shell made of a conductor. It has inner radius \(a\) and outer radius \(b\), and carries charge \(Q\). At its centre is a dipole \(\vec{p}\) as shown. In this case: