# 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????

148 Points
14 years ago

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

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askIITians Faculty 614 Points
3 years ago
charge at the segment rdθ =ardθ
The horizontal component of force is canceled out because a ring is symmetric about the y-axis.
A point charge is = q
Semicircular thread being  = R
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
Therefore the force required to keep the charge stationary = 2kqa/r