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Charge is distributed within a sphere of radius R with a volume charge density ρ (r) = –2r a 2 A e r , where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

1. a Q log 1 – 2 2 aA ⎛ ⎞ ⎜ ⎟ π ⎝ ⎠
2. a 1 log 1 – Q 2 2 aA ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ π ⎝ ⎠
3. 1 a log Q 1 – 2 aA ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ π ⎝ ⎠
4. Q a log 1 – 2 aA ⎛ ⎞ ⎜ ⎟ π ⎝ ⎠

Correct answer: a 1 log 1 – Q 2 2 aA ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ π ⎝ ⎠

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