Potential Energy of Two Point Charges

Q. A small metal sphere, carrying a net charge of $q_1=-2\mu C$, is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of $q_2=-8\mu C$ and mass $1.50g$ is projected towards $q_1$. When the two spheres are $0.800\text{m}$ apart, $q_2$ is moving towards $q_1$ with speed $20m{s}^{-1}$ as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.
How close does $q_2$ get to $q_1$?

1. $0.20\text{m}$
2. $0.30\text{m}$
3. $0.10\text{m}$
4. $0.15\text{m}$

Q. Four identical charged particles having same mass are located at four corners of a regular tetrahedron. If only one of the particles is released, with the remaining tetrahedron fixed, it acquires a final speed of $V_o.$ If all the charges are released together, their final speed will be $\frac{V_o}{n}$, then n is

Q. Two insulating plates are uniformly charged in such a way that potential difference between them is $V_2-V_1=20\text{V}$. Plates are separated by $d=0.1\text{m}$. An electron is released from rest in between the plates from the surface of plate $1$. What is its speed when it hits the plate $2$?
$($Charge on an electron, $e=-1.6\times {10}^{-19}\text{C}$ and mass of an electron, $m_e=9.1\times {10}^{-31}\text{kg})$

1. $1.87\times {10}^6\text{m/s}$
2. $32\times {10}^{-19}\text{m/s}$
   
3. $7.02\times {10}^{12}\text{m/s}$
4. $2.65\times {10}^6\text{m/s}$

Q.

There are two point charges of +1C each separated by 10m in vacuum. Calculate the change in potential energy of the system if they are brought to a separation of 5m.

1. $9\times {10}^{9}J$

2. $9\times {10}^{8}J$

3. $9\times {10}^{7}J$

4. None