wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

An annular disc has inner and outer radius R1​ and R2​ respectively. Charge is uniformly distributed. Surface charge density is σ. Find the electric field at any point distant y along the axis of the disc.


A
σy2ϵ0⎢ ⎢1R21+y21R22+y2⎥ ⎥
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
σ2ϵ0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
σy2ϵ0(R2R1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
σ2ϵ0logR2+yR1+y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A σy2ϵ0⎢ ⎢1R21+y21R22+y2⎥ ⎥

Consider a hypothetical ring of radius x and thickness dx on the disc.
The charge on the hypothetical ring :
dq=σ.2πxdx

Now the electric field at point P due to the ring is :

dE=dq4πϵ0×y(x2+y2)3/2

dE=σ.2πxdx4πϵ0×y(x2+y2)3/2

For complete annular disc,
E=dE=σy2ϵ0x(x2+y2)3/2dx

Let,
x2+y2=p22xdx=2pdp

x(x2+y2)3/2dx=pdpp3=1p

E=σy2ϵ0[1x2+y2]R2R1

E=σy2ϵ0⎢ ⎢1R21+y21R22+y2⎥ ⎥

flag
Suggest Corrections
thumbs-up
10
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Dielectrics
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon