# If BCD is semicircle arc in the plane of AB and DE with center at O and radius r and line DB makes angle a with a with DE then find the magnitude of magnetic induction produce at point O

WE know for  SEMIN INFINITE WIRE we have$\mu i/4\Pi d$...therefore it is  $\mu i/4\Pi r\sin\alpha$ ..  IT IS for one semi infinite wire for 2 semi infinite wire we have to multiply by 2 i.e.$2\mu i/4\Pi r\sin\alpha = \mu i/2\Pi r\sin \alpha$.......  Now   FOR SEMI CIRCLE IT IS $\mu i/4r$ eqn (2)     on adding both the magnetic field we get ….    $\mu i/2\Pi r\sin \alpha +\mu i/4r= \mu i/4\Pi r\left [ 2\csc \alpha +\Pi \right ]$  …....  since $[1/\sin \alpha =cosec \alpha ]$