When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:

Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart. C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is:
   
1. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
2. $\frac{qQ}{2{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
3. $\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
4. $-\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

Two charges q₁ and q₂ are placed 30 cm apart, as shown in the figure. A third charge q₃ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{\mathrm{q}}_3}{4\mathrm{\pi }{\in }_0}\mathrm{k}$ , where k is:

.

1. 8q₂

2. 6q₂

3. 8q₁

4. 6q₁

As per this diagram, a point charge \(\mathrm{+q}\) is placed at the origin \(\mathrm{O}.\) Work done in taking another point charge \(\mathrm{-Q}\) from the point \(\mathrm{A},\) coordinates \((\mathrm{0,a}),\) to another point \(\mathrm{B},\) coordinates \((\mathrm{a,0}),\) along the straight path \(\mathrm{AB}\) is:

If identical charges (–q) are placed at each corner of a cube of side 'b' then the electrical potential energy of charge (+q) which is placed at centre of the cube will be:

1. $\frac{-4\sqrt{2}{\mathrm{q}}^2}{{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

2. $\frac{-8\sqrt{2}{\mathrm{q}}^2}{{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

3. $\frac{-4{\mathrm{q}}^2}{\sqrt{3}{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

4. $\frac{8\sqrt{2}{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

A capacitor is charged with a battery and energy stored is U. After disconnecting the battery another capacitor of the same capacity is connected in parallel with it. The energy stored in each capacitor is:

1. U/2

2. U/4

3. 4 U

4. 2 U