A proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \,cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\,m / s$

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7}\; C$ located $9 \;cm$ away.

$(b)$ Hence obtain the work done in bringing a charge of $2 \times 10^{-9} \;C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

Choose the $CORRECT$ option

In the electric field of a point charge $q$, a certain charge is carried from point $A$ to $B$, $C$, $D$ and $E$. Then the work done

In the following diagram the work done in moving a point charge from point $P$ to point $A, B$ and $C$ is respectively as $W_A,\, W_B$ and $W_C$, then (there is no charge nearby)

This questions has statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly
positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement$ -1$ : When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by  $\frac{{q\rho }}{{3{\varepsilon _0}}}$

Statement$ -2$ : The electric field at a distance $r(r < R)$  from centre of the sphere is $\frac{{\rho r}}{{3{\varepsilon _0}}}$