Three semi-infinite rods uniformly charged out of which one is negatively charged and other two are positively charged are kept perpendicular to plane of paper outward such that the finite ends of the rods are located at points A, B and C on a circle of radius R as shown in figure. The net electric field at centre of circle O is :

Options

A. `(2 k lambda)/(R)` along OC
B. `(k lambda)/(R)`, perpendicular to plane of paper and inward direction
C. `(sqrt(5) k lambda)/(R)` at an angle `tan^(-1) (-1/2)` with OC
D. `(sqrt(2) k lambda)/(R)` at an angle `45^(@)` with OC

Answer

C

Explanation

One component of electric field at centre O is `(2k lamda)/R` along OC and other component is perpendicular to OC. Thus net electric field at point O is given as `E_(net)=(K lamda)/R sqrt5`
Resulting electric field at O is at an angle from OC where we have `tan theta =(K lamda//R)/(2k lamda//R)=1/2`