Figures (a) and (b) show the field lines of a positive and negative point charge respectively.

The signs of the potential difference $V_P-V_Q<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>V_B-V_A<mspace\; width="1em"></mspace>\mathrm{are}<mspace\; width="1em"></mspace>\mathrm{respectively}:$

$1.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>-$
$2.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>+$
$3.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>+$
$4.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>-$

Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The signs of the potential energy difference of a small negative charge between the points Q and P & A and B are respectively:
 

$1.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>-$
$2.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>+$
$3.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>+$
$4.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>-$

Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The sign of the work done by the field in moving a small positive charge from Q to P and the sign of the work done by the external agency in moving a small negative charge from B to A, respectively, will be:
 

$1.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>-$
$2.<mspace\; width="1em"></mspace>+,<mspace\; width="1em"></mspace>+$
$3.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>+$
$4.<mspace\; width="1em"></mspace>-,<mspace\; width="1em"></mspace>-$

Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The kinetic energy of a small negative charge in going from B to A:

1. decreases.

2. increases.

3. remains the same.

4. first increases and then decreases.

Four charges are arranged at the corners of a square ABCD of side d, as shown in the figure. The work required to put together this arrangement will be:

$1.<mspace\; width="1em"></mspace>\frac{-q^2}{4\pi {\epsilon }_{0}d}\left(4-\sqrt{2}\right)$
$2.<mspace\; width="1em"></mspace>\frac{-q^2}{4\pi {\epsilon }_{0}d}\left(2-\sqrt{2}\right)$
$3.<mspace\; width="1em"></mspace>\frac{-q^2}{4\pi {\epsilon }_{0}d}\left(4+\sqrt{2}\right)$
$4.<mspace\; width="1em"></mspace>\frac{-q^2}{4\pi {\epsilon }_{0}d}\left(2+\sqrt{2}\right)$

Four charges are arranged at the corners of a square \(ABCD\) of side \(d\), as shown in the figure. A charge \(q_0\) is brought from \(\infty\) to the centre \(E\) of the square, the four charges being held fixed at its corners. How much work is needed to do this?

1. \(\frac{-q^2}{4\pi\varepsilon_0 d}(4-\sqrt{2})\)
2. zero
3. \(\frac{-q^2}{4\pi\varepsilon_0 d}(4+\sqrt{2})\)
4. \(\frac{-q^2}{4\pi\varepsilon_0 d}(2+\sqrt{2})\)

The electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively is:

1. 0.2 J

2. -0.7 J

3. -0.2 J

4. 0.7 J

How much work is required to separate two charges  7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) infinitely away from each other?

1. 0.2 J

2. -0.7 J

3. -0.2 J

4. 0.7 J

The electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (in an external electric field E = A(1/r²); A = 9 × 10⁵ C m^–2) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively is:

1. 34 J

2. 49.3 J

3. 47 J

4. 43 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