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Offline Centres

A section of a uniformly charged spherical shell is as shown (surface charge density $= σ$ ). Its centre is O and A is a point on its parent sphere at the line of symmetry. Find electrostatic field at point A due to this charge arrangement.

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$\frac{σ}{2 ε_{0}} (1 - \sin θ)$

$\frac{σ}{2 ε_{0}} (1 - \cos (\frac{θ}{2}))$

$\frac{σ}{2 ε_{0}} (1 - \sin (\frac{θ}{2}))$

$\frac{σ}{2 ε_{0}} (1 - \cos θ)$

answer is C.

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Detailed Solution

$\int_{0}^{θ} \frac{K (σ (2 π R \sin θ) (R d θ))}{{(2 R \cos \frac{θ}{2})}^{2}} \cos \frac{θ}{2} = \frac{σ}{2 ε_{0}} (1 - \cos \frac{θ}{2})$

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