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