a point q charge is kept at the centre of the fixed semicircular thread having a uniform charge per unit length a,the radius of semicircular thread being r .the force required to keep the charge stationary is????

Dear jauneet

 

charge at the segment rdθ =ardθ

clearly horizontal component of force is cancel out because ring is symmetric about y axis

verticle force =Fcosθ =kqardθ/r²Cosθ

                               =kqa/r cosθ dθ

so total force = limit 0 to 90  ,  2∫ kqa/r cosθ dθ 

                    =limit 0 to 90  ,  2kqa/r∫ cosθ dθ 

                     = 2kqa/r

---

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin