Potential Energy of a System of Multiple Point Charges

Q. An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the x-axis at $x=1\text{m},x=2\text{m},x=4\text{m},x=8\text{m}$ and so on. Then the electrical potential at $x=0$ due to this set of charges is ( Assume that $\frac{1}{4\pi {ϵ}_0}=k$)

1. $2kq$
2. $\frac{2kq}{5}$
3. $\frac{4kq}{3}$
4. $\frac{4kq}{5}$

Q. Two Charges $Q_1$ and $Q_2$ are as shown in the figure. A third charge $Q_3$ is moved from points A to B along a circular path. Change in potential energy of the system is

1. $k{Q}_1{Q}_2{Q}_3$
2. $4k{Q}_1{Q}_2$
3. $4k{Q}_2{Q}_3$
4. $\frac{2}{3}k{Q}_2{Q}_3$

Q. Charges –q, Q and –q are placed at an equal distance on a straight line. If the total potential energy of the system of three charges is zero, then find the ratio $\frac{Q}{q}$.

Q. In the $\alpha -$particle scattering experiment, the foil should made of a metal having,

1. none of the above
2. any metal will do, irrespective of its atomic number
3. small atomic number
4. high atomic number