A point charge q lies on the axis of a square non-conducting surface, very close to its centre. The electric flux through the square due to q is Φ.The square is then given uniform surface charge density σ. The magnitude of force on q due to the charged square is:
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Question

A point charge q lies on the axis of a square non-conducting surface, very close to its centre. The electric flux through the square due to q is Φ.The square is then given uniform surface charge density σ. The magnitude of force on q due to the charged square is:

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G1 Physics · Accepted Answer

For the square, Φ = [q/(4πε₀)] ∫(cosθ/r²)dA. The electric field at q due to the uniformly charged square is E = [σ/(4πε₀)] ∫(cosθ/r²)dA. Therefore, E = (σ/q)Φ. Hence, F = qE = σΦ.