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The electric field intensity at the centre of a uniformly charged hemispherical shell is $E_{0} .$ Now two portions of the hemisphere are cut from either side and remaining portion is shown infigure. If $α = β = \frac{π}{3},$ then electric field intensity at centre due to remaining portion is $\frac{E_{0}}{n},$ find $n .$

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answer is 2.

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Detailed Solution

The magnitude of electric field intensity due to each part of the hemispherical surface at the centre 'O' is same. Suppose, It is E.
$E + \frac{E}{2} + \frac{E}{2} = E_{0}$
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$2 E = E_{0}$
$E = \frac{E_{0}}{2}$

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