Question

Consider a circular loop that is uniformly charged and has a radius $ \sqrt{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 the $ xy $-plane at the origin:

Hint:

For maximum electric field along the axis of a charged circular loop, set the derivative of the electric field with respect to \( x \) to zero.

Answer 1

Correct Answer: 3

\[ E = \frac{KQr}{(x^2 + R^2)^{3/2}} \] \[ \frac{dE}{dx} = 0 \] \[ \therefore x = \frac{R}{\sqrt{2}} = \sqrt{\frac{2a}{\sqrt{2}}} = a \] Thus, the value of \( x \) is \( a \), which corresponds to option (3).