JEE Main 2025 Apr 2 Shift 2, Physics Q20: Coulomb's Law And Electric Field

JEE Main2025Apr 2, Shift 2Physics

Consider a circular loop that is uniformly charged and has a radius $a 2$ . 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 $x y$ -plane at the origin :

A
$\frac{a}{2}$
B
$\frac{a}{2}$
C
$a$
D
$0$

Solution

For a uniformly charged ring of radius $R$ centred at the origin in the $x y$ -plane, the field on the axis at height $z$ is

$E (z) = \frac{k Q z}{( z ^{2} + R ^{2} ) ^{3/2}}$ .

Setting $\frac{d E}{d z} = 0$ gives the maximum at $z = \frac{R}{2}$ .

With $R = a 2$ : $z = \frac{a 2}{2} = a$ .

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JEE Main 2025 Apr 2 Shift 2, Physics Q20: Coulomb's Law And Electric Field

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