wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A solid sphere with uniform charge distribution, of self energy U0 and radius R is divided into n number of smaller spheres of radius r. The self energy of each smaller sphere is

A
U=U0n5/6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
UOn5/3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
UOn5/6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
U0n7/6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B UOn5/3
Let the charge on the solid sphere beQ and radius of the solid sphere beR

Self energy of a solid sphere U0=3kQ25R [k=14πε0]
Q2=5RU03k

Let the charge on each small sphere be q and the radius of each smaller sphere ber.

Self energy of each smaller sphere U=3kq25r .....(1)
From conservation of charge, we can write that
q=Qn ...(2)
Given that, Solid sphere is made into n smaller spheres

Thus, the volume remains constant,

43πR3=n×43πr3

r=(Rn1/3 ) .....(3)

From (1)) , (2) and (3) we can write that,

U=UOn5/3

Hence, option (b) is the correct answer.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon