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 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:
             
1. \( \frac{Q}{2 \pi a^2} \)
2. \(\frac{Q}{2 \pi\left(b^2-a^2\right)} \)
3. \(\frac{2 Q}{\pi\left(a^2-b^2\right)} \)
4. \(\frac{2 Q}{\pi a^2}\)

An electric dipole has a 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 \(\vec T_1 = \tau \hat k.\)$\stackrel{}{}$ When subjected to another electric field \(\vec E_2 = \sqrt{3}E_1 \hat j\)  it experiences a torque \(\vec T_2 = - \vec T_1.\)$\stackrel{}{}$The angle \(\theta\) is:
1. \(30^{\circ}\)
2. \(45^{\circ}\)
3. \(60^{\circ}\)
4. \(90^{\circ}\)

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. \( \tan ^{-1}(2.0)\)