A current I is flowing in a conductor shaped as shown in figure. The radius of the curved part is r and length of straight portion is very large. Find the magnetic field induction at the centre O.

Answer

`(mu_0I)/(4pir)((3pi)/(2)+1)`

Explanation

`vecB_0=vecB_(CD)+vecB_(DEF)+vecB_(FG)`, Here, `B_(CD)=0`,
`vecB_(DEF)=(mu_0)/(4pi)(3/4xx2piI)/(r)hatn`
and `vecB_(FG)=(mu_0)/(4pi)I/r[sin 90^@+sin0^@]hatn=(mu_0)/(4pi)I/rhatn`
`:. vecB_0=0+(mu_0)/(4pi)xx(3pi)/(2r)Ihatn+(mu_0)/(4pi)I/rhatn`
`=(mu_0)/(4pi)I/r((3pi)/(2)+1)hatn`
where `hatn` is a unit vector perpendicular to the plane of conductor outwards.