Answer:
[tex]x = 5.23 cm[/tex]
Explanation:
Here if the radius of the ring is R then electric field on its axis is given by the formula
[tex]E = \frac{kqx}{(x^2 + R^2)^{3/2}}[/tex]
now we know that if the electric field is maximum at a point on its axis then its differentiation with respect to the distance will be zero
so we have
[tex]\frac{dE}{dx} = 0[/tex]
[tex]0 = kq(\frac{1(x^2 + R^2)^{3/2} - x.3x(x^2 + R^2)^{1/2}}{(x^2 + R^2)^3})[/tex]
so we have
[tex](x^2 + R^2) - 3x^2 = 0[/tex]
[tex]x = \frac{R}{\sqrt2}[/tex]
so here we have
R = 7.40 cm
[tex]x = 5.23 cm[/tex]
