Point charge q moves from point P to point S along the path PQRS (figure shown) in a uniform electric field E pointing co-parallel to the positive direction of the x-axis. The coordinates of the points P, Q, R, and S are $(a,b,0),(2a,0,0),(a,-b,0)$ and (0, 0, 0) respectively. The work done by the field in the above process is given by the expression 

(1) qEa

(2) – qEa

(3) $qEa\sqrt{2}$

(4) $qE\sqrt{[{\left(2a\right)}^2+b^2]}$

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E.\) The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ}\)$$, the torque and the potential energy of the dipole will respectively be:
1. \(pE\text{sin}\theta, ~-pE\text{cos}\theta\)
2. \(pE\text{sin}\theta, ~-2pE\text{cos}\theta\)
3. \(pE\text{sin}\theta, ~2pE\text{cos}\theta\)
4. \(pE\text{cos}\theta, ~-pE\text{sin}\theta\)

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}.\) The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}. \) The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right) \)

An electric dipole of length 2 cm is placed with its axis making an angle of $30°$ to a uniform electric field ${10}^5<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{C}$. If it experiences a torque of $10\sqrt{3}<mspace\; width="1em"></mspace>\mathrm{Nm}$, then the potential energy of the dipole:

1. -10 J

2. -20 J

3. -30 J

4. -40 J

A molecule of a substance has a permanent electric dipole moment of magnitude 10^–29 C m. A mole of this substance is polarised (at low temperature) by applying a strong electrostatic field of magnitude 10⁶ V m^–1. The direction of the field is suddenly changed by an angle of ${60}^0$. The heat released by the substance in aligning its dipoles along the new direction of the field is: (For simplicity, assume 100% polarisation of the sample).

1. 6 J

2. 8 J

3. 3 J

4. 4 J

An electric dipole of moment p is placed parallel to the uniform electric field. The amount of work done in rotating the dipole by 90⁰ is-
1.  2pE
2.  pE
3.  pE/2
4.  Zero