Question

A circular ring of radius R and uniform linear charge density + l coulomb/metre are kept in x-y plane with its centre at origin. Electric field at point $\left( 0,0,\frac{R}{\sqrt{2}} \right)$is-

• A. $\frac{\lambda}{3\sqrt{3}\varepsilon_{0}R}$
• B. $\frac{2\lambda}{3\sqrt{3}R^{2}}$
• C. $\frac { 2 } { 3 \sqrt { 3 } }$ $\frac{\lambda}{\varepsilon_{0}R}$
• D. None of these

Answer 1

Answer: (A)

$\frac{\lambda}{3\sqrt{3}\varepsilon_{0}R}$

Answer 2

E_axis = $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\frac { \mathrm { qz } } { \left( \mathrm { R } ^ { 2 } + \mathrm { z } ^ { 2 } \right) ^ { 3 / 2 } }$ , at z =$\frac { \mathrm { R } } { \sqrt { 2 } }$

E_axis = $\frac { 2 } { 3 \sqrt { 3 } }$ $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\frac { \mathrm { q } } { \mathrm { R } ^ { 2 } }$

= $\frac { 2 } { 3 \sqrt { 3 } }$ .$\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$. $\frac { \lambda .2 \pi \mathrm { R } } { \mathrm { R } ^ { 2 } }$ = $\frac { \lambda } { 3 \sqrt { 3 } \varepsilon _ { 0 } R }$