A small circular ring has a uniform charge distribution. On a far-off axial point at a distance x from the centre of the ring, the electric field is proportional to :-x–1x–3/2x–2x5/4
Question
A small circular ring has a uniform charge distribution. On a far-off axial point at a distance x from the centre of the ring, the electric field is proportional to :-x–1x–3/2x–2x5/4
Solution
The electric field (E) due to a ring of charge at a point on the axis of the ring is given by the formula:
E = kQx / (x² + r²)^(3/2)
where:
- k is Coulomb's constant,
- Q is the total charge on the ring,
- x is the distance from the center of the ring to the point,
- r is the radius of the ring.
As the point is far off from the ring (x >> r), we can neglect r² in comparison to x². So, the formula simplifies to:
E = kQx / x³ = kQ / x²
Therefore, the electric field at a far-off axial point from the center of the ring is inversely proportional to the square of the distance from the center of the ring. So, the correct answer is x^-2.
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