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Using Gauss's law obtain the expression ...

Using Gauss's law obtain the expression for the electric field due to uniformly charged thin spherical shell of radius R at a point outside the shell. Draw a graph showing the variation of electric tield with r, for r gt R and r lt R.

Text Solution

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Electric fieldout side the shell `(r rarr R)`.
Let we have a spherical shell having +q charge on the surface, we have choosen a spherical Gaussian surface S. According to Gauss's theorem
`phi=underset(s)ointvecE. vec(ds)=(9)/(in_(0))`
`underset(s)oint cos 0^(@) =(q)/(in_(0)){{:("E is constant"),(oint ds = 4pir^(2)),(cos 0^(@) =1):}`
`E(4pir^(2))(1)=(q)/(in _(0))," "E=(1)/(4pi in_(0))(q)/(r^(2))`
It's equal to the electric field due to a point charge.
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Knowledge Check

  • The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre

    A
    `(Q)/(4 pi epsilon_(0)r)` for points outside and `(Q)/(4pi epsilon_(0)R)` for points inside the shell
    B
    `(Q)/(4pi epsilon_(0)e)` for both points inside nad outside the shell
    C
    zero for points outside and `(Q)/(4pi epsilon_(0)r)` for points inside the shell
    D
    zero for both points inside and outside the shell

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