Question

A ring with a uniform charge Q and radius R, is placed in the yz plane with its centre at the origin. Then :

• A. The field at the origin is zero
• B. The potential at the origin is $k\frac{Q}{R}$
• C. The field at the point (x, 0, 0) is $k\frac{Q}{x^2}$
• D. The field at the point (x, 0, 0) is $k\frac{Q}{R^2+x^2}$

Answer 1

Answer: (A), (B)

The correct options are
A The field at the origin is zero
B The potential at the origin is $k\frac{Q}{R}$

The electric field due to the ring at a point p on the axis of ring is $E=k\frac{Qz}{(z^2+R^2{)}^{3/2}}$
At center, $z=0,E=0$. Thus the electric field at the origin is zero.
As $E=-\frac{dV}{dz}$, the electric potential due to the ring at a point p on the axis of ring is $V=k\frac{Q}{\sqrt{z^2+R^2}}$
At center, $z=0,V=kQ/R$