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Surface density of charge on a sphere of...

Surface density of charge on a sphere of radius R in terms of electric intensity E at a distance in free space is
`(epsi_(0)` = permittivity of free space)

A

`(4pi kR^4)/(3 epsilon_0)`

B

`( kR)/(3 epsilon_0)`

C

`(4pi kR)/( epsilon_0)`

D

`( kR^2)/(4 epsilon_0)`

Text Solution

Verified by Experts

The correct Answer is:
D
Volume density `(rho)=kr`
Total charge `(q) = int rhodv = int_0^(R) kr 4pir^2 dr`
`q=4k[r^4/4]_0^R=(4kR^4)/(4)=kR^4`
According to Gaussian law
`ointvecE.vec(ds)=(q_("in"))/(epsilon_0)impliesExx4piR^2=(kR^4)/epsilon_0implies E=(kR^2)/(4 epsilon_0)`
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