A wire having a uniform linear charge density $λ$ is bent in the form of a ring of radius R. Point A as shown in figure is in the plane of the ring but not at the center. Two elements of the ring of lengths a₁ and a₂ subtend very small same angle at point A. They are at distances r₁ and r₂ from point A, respectively $(r_{2} > r_{1})$ .

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The ratio of charges of element a₁ to that of element a₂ is r₁/r₂.

The element a₁ produced greater magnitude of electric field at A than element a₂.

The elements a₁ and a₂ produce same potential at A.

The direction of the net electric field produced by the elements only at A is toward element a₂.

answer is A, B, C, D.

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Detailed Solution

Charge on $a_{1} is (r_{1} θ) λ$

Charge on $a_{2} is (r_{2} θ) λ$

Ratio of charges is $r_{1} / r_{2}$

$E_{1} (field produced by a_{1}) = \frac{K [(r_{1} θ) λ]}{r_{1}^{2}} = \frac{Kθλ}{r_{1}}$

$E_{2} (field produced by a_{2}) = \frac{Kθλ}{r_{2}}$

$As r_{2} > r_{1}, E_{1} > E_{2} i.e., net field at A is toward a_{2}$ .

$V_{1} = \frac{K (r_{1} θ)}{r_{1}} = Kθλ$

$V_{1} = V_{2}$

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