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. \(\frac{- 4 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\)

2. \(\frac{- 8 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\)

3. \(\frac{- 4 q^{2}}{\sqrt{3} \pi\varepsilon_{0} b}\)

4. \(\frac{8 \sqrt{2} q^{2}}{4 \pi\varepsilon_{0} b}\)

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: