A ring of radius R has charge -Q distributed uniformly over it- Calculate the charge that should be placed the center of the ring such that the electric field becomes zero a point on the axis of the ring distant R from the center of the ring

Question

Toppr Admin · Accepted Answer

Electric field at point P due to charge of ring is
$E = \frac{k Q x}{(R^{2} + x^{2})^{3 / 2}}$
At $x = R, E = \frac{k Q}{2 \sqrt{2} R^{2}}$ directed toward the center.
Electric field at P due to charge at center $k q / R^{2}$
For net field to be zero at P.
$\frac{k q}{R^{2}} = \frac{k Q}{2 \sqrt{2} R^{2}}$ or $q = \frac{Q}{2 \sqrt{2}}$

A ring of radius R has charge -Q distributed uniformly over it. Calculate the charge that should be placed at the center of the ring such that the electric field becomes zero at a point on the axis of the ring at distant R from the center of the ring

Electric field at point P due to charge of ring isE=kQx(R2+x2)3/2At x=R,E=kQ2√2R2 directed toward the center.Electric field at P due to charge at center kq/R2For net field to be zero at P.kqR2=kQ2√2R2 or q=Q2√2