A large straight current carrying conductor is bent in the form of L shape. Find `vecB`at P.

Explanation

Let us divide the conductor into two semi infinite segments 1 and 2. Then, induction at P is
` vecB = vecB_1 + vec B_2`
`vecB_1 = (mu_0 i)/(4pi a) (sin (90^@ - theta_1) + sin 90^@) hatk " " …..(ii)`
`vecB_2 = (mu_0 i)/(4pi a) (sin (90^@ - theta_2) + sin 90^@ ) hatk " "...(iii)`
then ` vecB = (mu_0i)/(4pi a) (cos theta_1 + cos theta_2 + 2) hatk, ` where
`cos theta_1 = cos theta_2 = (1)/(sqrt2) " hence " , vecB = (2 + sqrt2) (mu_0 i hatk)/(4pi a)`