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Q.

A region in space contains a total positive charge Q that is distributed spherically such that the volume charge densityρ(r)=α for r≤R22α1−rR for R2≤r≤R0 for r≥RWhere a is a positive constant. The value of a in terms of Q and R is

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a

3QπR38

b

8QπR35

c

8Q5πR3

d

8Q8πR3

answer is C.

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Detailed Solution

Q=∫0R/24πr2⋅dr⋅α+∫R2R2α1−rR4πr2dr=παR36+11παR324=58παR3​⇒a=8Q5πR3
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A region in space contains a total positive charge Q that is distributed spherically such that the volume charge densityρ(r)=α for r≤R22α1−rR for R2≤r≤R0 for r≥RWhere a is a positive constant. The value of a in terms of Q and R is