Question

A uniformly charged ring of radius \( R \) carries total charge \( Q \). Find the electric field at a point on the axis at a distance \( x = \frac{R}{\sqrt{2}} \) from the center.

• A. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{Qx}{(R^2 + x^2)^{3/2}} \)
• B. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{QR}{(R^2 + x^2)^{3/2}} \)
• C. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{Q}{R^2} \)
• D. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{Q}{(2R^2)^{3/2}} \)

Hint:

\textbf{Tip:} For field on the axis of a ring, only the axial components add; radial components cancel due to symmetry.