A long straight wire carrying electric current i is bent at its mid-point to form an angle of `45^(@)` as shown in the figure. Magnetic field at a point P at a distance d from the point Q of bending is

Options

A. `(mu_(0)i)/(4pi d)[sqrt2-1]`
B. `(mu_(0)i)/(2pi d)[sqrt2-1]`
C. `(mu_(0)i)/(4pi d)`
D. `(mu_(0)i)/(2pi d)`

Answer

A

Explanation

Magnetic field at a point from a current carrying conductor making angle `theta_(1) and theta_(2)` with the ends of wire is given using Bio-Savart.s law as
`B = (mu_(0)I)/(4pi r) (sin theta_(1) + sin theta_(2))`
`= (mu_(0)I)/(4pi ((d)/(sqrt2))) [sin 90^(@) + sin 135^(@)]`
`=(sqrt2mu_(0)I)/(4pi d) (1-(1)/(sqrt2)) = (mu_(0)I)/(4pi d) (sqrt2-1)`