Current I is flowing in a conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre will be

Options

A. `mu_(0)/(4pir)((pi)/(2)+1)`
B. `mu_(0)/(4pir)((pi)/(2)-1)`
C. `mu_(0)/(4pir)((3pi)/(2)+1)`
D. `mu_(0)/(4pir)((3pi)/(2)-1)`

Answer

C

Explanation

For the circular part BCD the angle subtended at the centre O is `3pi"/"2)`.
Total magnetic field at dO is
`=B_(AB)+B_(BCD)+B_(DE)=(mu_(0))/(4pi)(i)/(r)[sin90^(@)+sin0^(@)]+(mu_(0))/(4pi)xx(3pi)/(2)+0`
`=(mu_(0))/(4pi)(i)/(r)+(mu_(0))/(4pi)(I)/(r)xx(3pi)/(2)=(mu_(0))/(4pi)(I)/(r)(1+(3pi)/(2))`