Question

In an oil drop experiment, charged oil drops of mass m and charge q are released at a height h, one at
a time, at intervals ∆t >
square root
2h/g. The drops are collected in a large metal sphere of radius R with a
small opening at the top. The total number of drops that are able to enter the sphere will be

Answer 1

ok,we have to suposse volume of sphere is much higher than the drop.
when drop hit the sphere,consider all of his charge flow to sphere, the charge must be much far from other as possible,so they will be distribuited along the sphere area.We know can be porved by the Gauss law all of this charge acts like they were in the center of sphere.
When the electrical force be equal to the eletrical the drop will not fail.

Answer 2

time to drop reach the "floor"
\[h=1/2*g*t^{2}\rightarrow t=\sqrt{2h/g}\]
\[Fe=K*qd*Qs/(h-r)^{2}\]
\[Qs=Nd*qd\]\[\rightarrow\]
\[K*qd*N*qd/(h-r)^{2}=m*g\]
\[N=(h-r)^{2}*m*g/qd^{2}*K\]