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For spherically symmetrical charge distr...

For spherically symmetrical charge distribution, electric field at a distance r from the centre of sphere is `vec(E)=kr^(7) vec(r)`, where k is a constant. What will be the volume charge density at a distance r from the centre of sphere?

A

`rho=9k epsilon_(0)r^(6)`

B

`rho=5k epsilon_(0)r^(3)`

C

`rho=3k epsilon_(0)r^(6)`

D

`rho=9k epsilon_(0)r^(0)`

Text Solution

Verified by Experts

The correct Answer is:
A
By using Gauss law `oint vec(E).dvec(S)=q/in_(0)rArr(E)(4pi r^(2))=(int rho(4pir^(2)dr))/in_(0)`
(Note: Check dimensionally that `rho prop r^(6)`)
`(kr^(7))(4pi r^(2))=(oint rho(4pir^(2)dr))/in_(0)rArr kepsilon_(0)r^(9)=int rho r^(2)drrArr rho=3k in_(0) r^(6)`
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Knowledge Check

  • A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre

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    B
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