A charged particle $\text{'}q\text{'}$ is shot towards another charged particle $\text{'}Q\text{'},$ which is fixed, with a speed $\text{'}v\text{'}.$ It approaches $\text{'}Q\text{'}$ up to a closest distance $r$ and then returns. If $q$ were given a speed $\text{'}2v\text{'},$ the closest distance of approach would be:

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2-V_1=20 \mathrm{V}.$ (i.e. plate $2$ is at a higher potential). The plates are separated by $d=0.1 \mathrm{m}$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1.$ What is its speed when it hits plate $2?$ $\left(e=1.6\times {10}^{-19}\mathrm{C}, m_e=9.11\times {10}^{-31} \mathrm{kg}\right)$

For an infinite line of charge having charge density $\lambda$ lying along $x$-axis, the work required in moving charge $q$ from $C$ to $A$ along the arc $CA$ is: