Question

A ring with a uniform charge $Q$ and radius $R$, is placed in the $y-z$ plane with its centre at the origin$(k=\frac{1}{4\pi {\epsilon }_0})$. Then :

• A. the field at the origin is not equal to 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: (B)

the potential at the origin is $k\frac{Q}{R}$

We know potential due to ${\upsilon }_1$ at a distance $r_1,v_1=\frac{k{v}_1}{r_1}$
Now as Q is placed at distance R from centre
$\therefore$ Potential at the centre$=\frac{kQ}{\sqrt{R^2}}=\frac{kQ}{R}$