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)/(2 pi R) (pi + 1)`
B. `(mu_(0)I)/(4 pi R) (pi^(2) + 1)`
C. `(mu_(0)I)/(4 pi R) (pi - 1)`
D. `(mu_(0)I)/(4 pi R) (pi + 1)`

Answer

D

Explanation

The portion of the wire through DE if extended backwards passes through the point O and hence it will not produce any magnetic field at point O. AB is semi-infinite wire for the point o and there is one half circle after point B, both are producing magnetic field inwards per the direction of the current, hence to calculate the net magnetic field, both of these fields will be added. Net magnetic field at the point O can be written as:
`B = (mu_(0)I)/(4R) + (mu_(0)I)/(4 pi R) = (mu_(0)I)/(4 pi R) (pi + 1)`
Hence, option (d) is correct.