16. A circular ring carries a charge Q, the variation of electric field with distance x measured from centre along axis
for x < <R can be given as R Radius of Ring
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electric field along axis of circular ring is given by,
where, x is observation point along axis of circular ring and r is the radius of ring.
differentiating electric field with respect to x,
for maximum electric field,
r² = 2x²
or, x = ± r/√2
hence, there are two optimum points,
for getting which point value of x for maximum again differentiating with respect to x. and putting both the value.
you will get, at x = r/√2
so, maximum value of electric field at X = r/√2
so, = kq(r/√2)/(r²/2 + r²)^{3/2}
= kqr/{√2(r² + 2r²)^{3/2}/2√2}
= 2kqr/(3r²)^{3/2}
= 2kqr/(3√3r³)
= 2kq/3√3r²
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