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

A solid conducting sphere of radius a having charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. If the amount of heat produced when switch is closed is α(Kq224a). Fill the value of α.
795946_5cb917a5a70040f6bee0d02d0ef2417d.png

Open in App
Solution

Capacitance of a spherical capacitor having inner radius of sphere a radius of outer sphere b is
C=abK(ba)
As b
C=aK
And energy of capacitor =q22C
Before closing the switch charge distribution is given by.
Total energy of system = Energy of capacitor (1)+ Energy of capacitor (2)
Capacitance of 1st capacitor C1=a×2aK(2aa)=2aK
Capacitance of 2nd capacitor C2=3aK
Total energy =q22(2aK)+q22(3aK)
T.Ei=Kq24a+Kq26a
After closing the switch charge distribution is as shown in Fig 3
Total energy =0+q22(3aK)
T.Ef=Kq26a
T.E=Kq24a=T.EfT.Ef
Thus heat produced =+Kq24a
If the amount of heat produced when switch is closed is 6(Kq224a)
Then α=6

957314_795946_ans_89514a96ae9b49138e3ef89a71f31886.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Thermal Expansion
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon