Q 12-01-160JEE MainJEE Main 2025 (2 Apr, Shift 2)Medium
Consider a circular loop that is uniformly charged and has a radius $a\sqrt2$. Find the position along the positive $z$-axis of the Cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in the $xy$-plane at the origin:
Answer: (C) $a$
On the axis of a ring of radius $R$ and charge $Q$:
$$E(z) = \frac{kQz}{(z^2 + R^2)^{3/2}}$$
$$\frac{dE}{dz} = kQ\,\frac{(z^2 + R^2) - 3z^2}{(z^2 + R^2)^{5/2}} = 0 \Rightarrow z = \frac{R}{\sqrt2}$$
With $R = a\sqrt2$, the field is maximum at $z = a$.
Solution by Sreeraj P, M.Sc Physics