CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A capacitor is made of two square plates each of side a making a very small angle a between them, as shown in figure. The capacitance will be close to



A
ϵ0 a2d(13αa2d)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
ϵ0 a2d(1αa4d)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ϵ0 a2d(1+αad)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ϵ0 a2d(1αa2d)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D ϵ0 a2d(1αa2d)

Consider an infinitesimal strip of capacitor of thickness dx at a distance x as shown

Capacitance of parallel plate capacitor of area A is given by C=ϵ0At

[Here t = seperation between plates]

So, capacitance of thickness dx will be

dC=ϵ0adxd+xtanα

Total capacitance of system can be obtained by integrating with limits x=0 to x=a


Ceq= dC=aϵ0 a0dxxtanα+d

[By binomial expansion]

Ceq=aϵ0da0(1xtanαd)dx=aϵ0d(xx2tanα2d)a0

Ceq=a2ϵ0d(1atanα2d)=ϵ0a2d(1αa2d)

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Magnetic Field Due to a Current Carrying Wire
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon