Name: Continuous Charge Distribution
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: This video will help us understand the necessity of continuous charge distribution and learn about the concept of linear charge density. Learn more.

Question

Electrically charged drops of mercury fall from altitude

h

into a spherical metal vessel of radius

R

in the upper part of which there is a small opening. The mass of each drop is

m

& charge is

Q

. What is the number '

n

' of last drop that can still enter the sphere.

Accepted Answer

Electric field by the conducting sphere, when $n = 1$ charge is dropped inside $=$ electric field due to conductivity sphere

$E = \frac{Q}{4 π ϵ_{0} {(h - R)}^{2}}$

Therefore, Electric field by the conducting sphere when n drops are fallen inside it. $E = \frac{Q n}{4 π ϵ_{0} {(h - R)}^{2}}$

Force on $(n + 1) th$ drop will be

$F = \frac{n Q \times Q}{4 π ϵ_{0} {(h - R)}^{2}}$

$F = \frac{n Q^{2}}{4 π ϵ_{0} {(h - R)}^{2}}$

As force is given by $F = m a$

Therefore,

$m a = \frac{n Q^{2}}{4 π ϵ_{0} {(h - R)}^{2}} a = \frac{n Q^{2}}{4 π ϵ_{0} {(h - R)}^{2} m}$

So, $(n + 1) t h$ drop will stop falling when $a = g$

therefore,

$g = \frac{n Q^{2}}{4 π ϵ_{0} {(h - R)}^{2} m}$

Thus,

$n = \frac{4 π ϵ_{0} m g (h - R) R}{Q^{2}}$

Electrically charged drops of mercury fall from altitude $h$ into a spherical metal vessel of radius $R$ in the upper part of which there is a small opening. The mass of each drop is $m$ & charge is $Q$ . What is the number ' $n$ ' of last drop that can still enter the sphere.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

Electrically charged drops of mercury fall from altitude h into a spherical metal vessel of radius R in the upper part of which there is a small opening. The mass of each drop is m & charge is Q. What is the number 'n' of last drop that can still enter the sphere.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

Electrically charged drops of mercury fall from altitude $h$ into a spherical metal vessel of radius $R$ in the upper part of which there is a small opening. The mass of each drop is $m$ & charge is $Q$ . What is the number ' $n$ ' of last drop that can still enter the sphere.