An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is V metre. The magnetic induction at the centre of the circular part is-

Options

A. `(mu_(0)I)/(4pi) (pi-1)`
B. `(mu_(0)i)/(2a) (1- 1/pi)`
C. `(mu_(0)i)/(2a) (pi-1)`
D. `(mu_(0)i)/(4a) (1- 1/pi)`

Answer

B

Explanation

Magnetic field due to current in straight wire `B_(1) = (mu_(0)i)/(2pia)`
(upwards `bot` to the page) and due to the circular current loop.

`B_(2) = (mu_(0)i)/(2a)` (downards `bot` to the page)
Directions of `B_(1)` and `B_2` may be observed with the right hand screw rule.
Now resultant field at C is:
`B = B_(2) - B_(1)` (Here `B_(2) gt B_(1)`)
`therefore B = B_(2) - B_(1) = (mu_(0)i)/(2a) (1- 1/pi)`
Hence, the correct answer is option (2).