Question

A small circular 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?

Answer 1

let the total charge on the ring is Q then

electric field at the axis of a charged ring is given by

E=kQx/(R² + x²)^3/2

Where, X -->distance of the point from center of ring

R--> Radius of ring

When, point is far away from the ring, X>>>R

Therefore R can be neglated.

Then,

E = KQx/ x^3

E = kQ/x^2 (one x is cancelled in numerator and denominator)

Therefore, E proportional to X ^(-2) or inversely proportional to x^2