A long wire carrying current 'I' is bent into the shape as shown in the figure. The net magnetic field intensity at the centre 'O' is

Options

A. `(mu_(0)I)/(4piR)sqrt(1 + pi^(2))`
B. `(mu_(0)I)/(4piR)sqrt(2 + pi^(2))`
C. `(mu_(0)I)/(4piR)sqrt(4 + pi^(2))`
D. `(mu_(0)I)/(4piR)sqrt(9 + pi^(2))`

Answer

A

Explanation

The net magnetic field intensity at the centre 'O' is
`vec(B_(0)) = (mu_(0)I)/(4piR) (-hat(k)) + (mu_(0)I)/(4R) (-hat(i))`
`:. B_(0) = (mu_(0)I)/(4piR) sqrt(1 + pi^(2))`