A charged particle having a positive charge q approaches a grounded metallic neutral sphere of radius R with a constant speed v as shown in figure. Now choose the correct alterative (s). 

 

The potential of the grounded sphere has to be zero, Due to point charge the potential of the sphere is positive so negative charge must be possessed by sphere so that total potential of sphere becomes zero. This negative charge is acquired by sphere from the ground hence current flows in to the ground. As the point charge comes nearer to sphere the potential of sphere due to positive charge increases and hence more electron per unit time will flow from ground to sphere and thus magnitude of current increases. 

$\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R}+\frac{1}{4\pi {\epsilon }_0}\frac{q}{\left(R_0-vt\right)}=0$

where $R_0$ is the initial distance of the charge particle, and Q is the charge on sphere at time t, 

$\Rightarrow Q=\frac{Rq}{R_0-vt}\Rightarrow \frac{dQ}{dt}=i=\frac{Rqv}{{\left(R_0-vt\right)}^2}$