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

A sphere is uniformly charged with charge per unit volume as ρ and radius R. The electrostatic potential energy stored inside the sphere is 4πρ2R5nϵ0. Fill the value of n

A
90.0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
90.00
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
90
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

As we know that energy per unit volume of a conductor is given by, dUdV=12ϵ0E2 ....(1)

Now energy stored inside a solid sphere:
Let us assume that a small element of dr thickness at a distance r from point O.



Electric field at point P, E=KQR3.r
From equation (1) energy of small element,
dU=12ϵ0E2dV

dU=12ϵ0(KQR3.r)2.4πr2.dr

Now total energy of solid sphere-
U=R0dU=4πϵ0Q2K22R6R0r4.dr

U=4πϵ02R6.Q216π2ϵ20[r55]R0=4πQ2R510ϵ016π2R6

U=4πR510ϵ0.Q216π2R69×9=4πR590ϵ0(QV)2⎪ ⎪ ⎪⎪ ⎪ ⎪ρ=QV=Q43πR3⎪ ⎪ ⎪⎪ ⎪ ⎪

U=4πρ2R590ϵ0=4πρ2R5nϵ0

n=90

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Energy of a Capacitor
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon