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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 density
ρ = κra, where κ and a are constants and r is the distance from its centre. If the electric
field 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)


 


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Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

7 years ago
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