A small circle ring has a uniform charge distribution. On a far-off axial point distance $x$ from the centre of the ring, the electric field is proportional to:

x^{- 1}

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x^{- 3 / 2}

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x^{- 2}

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x^{5 / 4}

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Solution

The correct option is C $x^{- 2}$
Electronic field due to a charged ring in given by :-
at point p
$∣ ∣ \to E ∣ ∣ = \frac{K Q x}{(R^{2} + x^{2})^{3 / 2}} Q = λ (2 π r)$
at a large distance, $x ≫ R,$ so :- $R^{2} + x^{2} ≃ x^{2}$
$\Rightarrow ∣ ∣ \to E ∣ ∣ = \frac{K & x}{(x^{2})^{3 / 2}} = \frac{K Q}{x^{2}} = E α x^{- 2}$
so at large distance, ring behave an a point particle.

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A small circle ring has a uniform charge distribution. On a far-off axial point distance x from the centre of the ring, the electric field is proportional to:

The correct option is C x−2Electronic field due to a charged ring in given by :-at point p∣∣→E∣∣=KQx(R2+x2)3/2Q=λ(2πr)at a large distance, x≫R, so :- R2+x2≃x2⇒∣∣→E∣∣=K&x(x2)3/2=KQx2=Eαx−2so at large distance, ring behave an a point particle.

A small circle ring has a uniform charge distribution. On a far-off axial point distance $x$ from the centre of the ring, the electric field is proportional to: