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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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(a) Use Gauss's law to show that due to a uniformly charged spherical shell of radius R, the electric field at any point situated outside the shell at a distance r from its centre is equal to the electric field at the same point, when the entire charge on the shell were concentrated at its centre. Also plot the graph showing the variation of electric field with r, for r le R and r ge R . (b) Two point charges of +1 muC and +4 muC are kept 30 cm apart. How far from the +1muC charge on the line joining the two charges, will the net electric field be zero ?

(a) Using Gauss's law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density sigma C//m^(2) . Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative. (b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 mu C//m^(2) . Calculate the (i) charge on the sphere (ii) total electric flux passing through the sphere.

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