The largest magnitude the electric field on the axis of a uniformly charged ring of radius 3m is at a distance h from its centre. What is the value of h? (Take `(1)/(sqrt(2))=0.7`)

Answer

`2.1`

Explanation

`E _("axial") = ( Qh )/(4 pi epsi _(0) ( h ^(2) + a ^(2)) ^((3)/(2)))`
where,
a = radius of the ring,
h = distance of point from the centre.
For the maximum value,
`(dE)/(dh) = 0`
`therefore (d)/(dh) [ (Qx)/( 4 pi epsi _(0) ( h ^(2) + a^(2)) ^((3)/(2))) ] =0`
`therefore (( h ^(2) + a ^(2)) ^((3)/(2)) - h ((3)/(2)) ( h ^(2) + a ^(2)) ^((1)/(2)). (2h))/(( h ^(2) + a ^(2)) ^(3)) = 0`
`therefore ( h ^(2) + a ^(2)) - 3h ^(2) =0`
`therefore h = pm (a)/( sqrt2)`
`= (3)/(sqrt2) m ....(because a = 3m )`
`= 3xx 0.7 = 2.1 m`