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anantika success shakya Grade: 12
`        A solid sphere of radius R has a charge Q distributed in its volume with a charge densityρ = κra, where κ and a are constants and r is the distance from its centre. If the electricfield at r =R/2  is 1/8  times that at r = R, find the value of a."`
7 years ago

## Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
```										Dear Anantika Shakya,
Ans:- The total charge is Q. Hence if we integrate the charge we shall get Q
Let us consider a thin spherical shell of thickness dr it'vol is 4∏r² dr and charge will be kra times of this hence From Gauss's law we get the value of the field at r=R/2 is
E 4∏(R/2)²=∫4∏kar³ dr=∏ka(R/2)^4
E=kaR²/16ε...............(1)
again the field at r=R is =Q/4∏R²ε...............(2)
The ratio is 1:8 hence we get
a=Q/(2∏kR^4)

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.
All the best Anantika Shakya !!!

Regards,
Askiitians ExpertsSoumyajit Das IIT Kharagpur
```
7 years ago
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