A charge praticle of charge q is kept at the centre of the semicircular charged, ring . If linear charge density is `lambda` every where, as shown in the figure. Then net electrostatic force on the particle is -

Options

A. `(lambdaq)/(4piepsi_(0)R)`
B. ` (sqrt(5)lambdaq)/(4piepsi_(0)R)`
C. ` (3lambdaq)/(4piepsi_(0)R)`
D. `(sqrt(2)lambdaq)/(4piespi_(0)R)`

Answer

B

Explanation

Due to rod only
`vecF_(1)=(lambdaq)/(4piepsi_(0)R)`
Due to semicircle only
`vecF_(2)=(lambdaq)/(2piepsi_(0)R)`
`F_("net")sqrt(F_(1)^(2)+F_(2)^(2))rArrF_("net")=sqrt(5lambda_(q))/(4piepsi_(0)R)`