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A solid sphere of radius R has a charge ...

A solid sphere of radius R has a charge Q distributed in its volume with a charge density `rho=kr^a`, where k 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 `r=R`, find the value of a.

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The correct Answer is:
2
`E(4pi r^(2))=int((kr^(a))4pir^(2)dr)/in_(0)`
`E(r^(2))=(int r^(a+2) dr)/in_(0)`
`rArr E(r^(2))=r^(a+3)/((a+3)in_(0))rArr E=r^(a+1)/((a+3)in_(0))`
`rArr E(R//2)=E 1/8 E(R)rArr (R/2)^(a+1)=1/8(R)`
`rArr 2^(a+1)=2^(3)rArr a=2`
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