Question

A conducting liquid drop has charge uniformly dis-

tributed over the surface. Electrostatic energy of drop

E0

. Now this drop is broken in 8 small liquid drops

such that mass and charge get equally distributed.

What is the change in electrostatic energy of the sys-

tem is the process. Assume drops to be widely sepa-

rated after break up.

A]0
B]-3E0/4
C]E0/2
D]3E0/4





​

Answer 1

Answer:

B

potential becomes n

2/3

times and charge density increases to n

1/3

times original charge density

Volume of n small drops is equal to that of the big drop

n×

3

4

πr

3

=

3

4

πR

3

⇒nr

3

=R

3

Let each drop has a surface charge density σ.

Therefore,

V

smalldrop

=

(4πϵ

0

)

1

×

r

σ4πr

2

=

ϵ

0

σr

.

Now, nσ4πr

2

=x4πR

2

⇒n×n

3

−2

=

σ

x

x=n

3

1

σ

Also,potential on big drop =

R

k×n×σ4πr

2

=

ϵ

0

n

×

(n

3

1

r)

r

2

=n

3

2

V