The unit vectors `hati, hatj` and `hatk` are as shown below. What will be the magnetic field at `O` in the following figure

Options

A. `mu_(0)/(4pi) i/a (2-pi/2) hatj`
B. `mu_(0)/(4pi) i/a (2+pi/2)hatj`
C. `mu_(0)/(4pi) i/a (2+pi/2)hati`
D. `mu_(0)/(4pi) i/a(2+pi/2) hatk`

Answer

D

Explanation

The field at 0 due to AB is `mu_(0)/(4pi). i.a hatk` and that due to DE is also `(mu_(0))/(4pi). i/a hatk`
However, the field due to BCD is `(mu_(0))/(4pi). i/a (pi/2) hatk`
Thus, the total field at O is `mu_(0)/(4pi). i/a (2+pi/2)hatk`