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The electric field intensity in free spa...

The electric field intensity in free space at a distance 'r' outside a charged conducting sphere of radius 'R' in terms of surface charge density `sigma` is

A

`(sigma)/(epsi_(0))[(R)/(r)]^(2)`

B

`(epsi_(0))/(sigma)[(R)/(r)]^(2)`

C

`(R)/(r)[(sigma)/(epsi_0)]^(2)`

D

`(R)/(sigma)[(r)/(epsi_(0))]^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
The electric field intensity at a point at a distance r outside
a charged conducting sphere is `E=(1)/(4piepsi_(0))(q)/(r^(2))` . .. (1)
where `r gt R`.
But surface charge density `(sigma)` of the sphere is
`sigma=(q)/(4piR^(2))" "therefore q=4piR^(2)sigma`
From (1), `E=(1)/(4piepsi_(0))(4piR^(2)sigma)/(r^(2)) =(sigma)/(epsi_(0))[(R)/(r)]^(2)`
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Knowledge Check

  • Electric field intensity in free space at a distance r outside the charged conducting sphere of radius R in terms of surface charge density sigma is

    A
    `sigma/epsi_(0)[R/r]^2`
    B
    `epsi_(0)/sigma[R/r]^2`
    C
    `R/r[sigma/epsi_(0)]^2`
    D
    `R/sigma[r/epsi_(0)]^2`

  • The magnitude of an electric intensity at a point which is at a distance 'r' from the centre of a charged spherical conductor of radius 'R' in terms of the surface charge density 'sigma' is given by 'E' where

    A
    `E=(sigma)/(Kepsi_(0)r^(2))`
    B
    `E=(sigmaR)/(Kepsi_(0)r^(2))`
    C
    `E=(sigmaR^(2))/(Kepsi_(0)r^(2))`
    D
    `E=(sigma^(2)R)/(Kepsi_(0)r^(2))`

  • The electric intensity at a point near a charged conductor of surface charge density sigma is

    A
    `E=sigma//in_(0)k`
    B
    `E=sigmain_(0)k`
    C
    `E=sigma//2in_(0)k`
    D
    `E=sigma^(2)`

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