A total charge Q is uniformly distributed on a circular arc of radius R subtending angle θ at the centre. The electric field magnitude at the centre is:
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A total charge Q is uniformly distributed on a circular arc of radius R subtending angle θ at the centre. The electric field magnitude at the centre is:

G1 Physics · Accepted Answer

Here the total charge Q is fixed, so λ = Q/(Rθ). Using the arc-field formula, E = (2kλ/R) sin(θ/2) = [2kQ/(R²θ)] sin(θ/2). As θ → 0, sin(θ/2) ≈ θ/2, so E → kQ/R², which is the field of a point charge Q at distance R.