The magnetic field at the origin due to the current flowing in the wire is

Options

A. `-(mu_(0)I)/(8pia)(hat(i)+hat(k))`
B. `(mu_(0)I)/(2pia)(hat(i)+hat(k))`
C. `(mu_(0)I)/(8pia)(-hat(i)+hat(k))`
D. `(mu_(0)I)/(4piasqrt(2))(hat(i)-hat(k))`

Answer

C

Explanation

`B_(OD) = 0`
`B_(OB) = 0`
`B_(AB) = (mu_(0)I)/(4piasqrt(2))(cos 45^(@)(-hat(i)-cos 45^(@)hat(k))`
`= (mu_(0)I)/(8pia)(-hat(i)+hat(k))`