A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density
$ρ (r) = \{\begin{array}{ccc} α & for & r \leq \frac{R}{2} \\ 2 α [1 - \frac{r}{R}] & for & \frac{R}{2} \leq r \leq R \\ 0 & for & r \geq R \end{array}$
Where a is a positive constant. The value of a in terms of Q and R is

Question

A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density

$ρ (r) = \{\begin{array}{ccc} α & for & r \leq \frac{R}{2} \\ 2 α [1 - \frac{r}{R}] & for & \frac{R}{2} \leq r \leq R \\ 0 & for & r \geq R \end{array}$

Where a is a positive constant. The value of a in terms of Q and R is

Infinity Learn · Accepted Answer

$$Q=$$∫$$0R/24$$$$π$$$$r2$$⋅dr⋅α$$+$$∫$$R2R2$$α$$1$$−$$rR4$$$$π$$$$r2dr=$$πα$$R36+11$$πα$$R324=58$$πα$$R3$$​⇒$$a=8Q5$$$$π$$$$R3$$

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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

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