Current I flows through a long conducting wire bent at right angle as shown in Fig. Find the magnetic field at point P on the right angle bisector of the angle XOY at distance r form O.

Options

A. `(mu_0I)/(pir)`
B. `(2mu_0I)/(pir)`
C. `(mu_0I)/(4pir)(sqrt2+1)`
D. `(mu_0)/(4pi)(2I)/(r)(sqrt2+1)`

Answer

D

Explanation

Magnetic field at P due to current through CO is same as that due to current through OD.

`:.` Total magnetic field at P due to currents through
CO and OD is
`B=B_(CO)+B_(OD)=2B_(CO)` [`:' B_(CO)=B_(OD)`]
`=2xx(mu_0)/(4pi)(I)/((r//sqrt2))[sin 45^@+sin 90^@]`
`=(mu_0)/(4pi)(2I)/(r)sqrt2[1/sqrt2+1]=(mu_0)/(4pi)(2I)/(r)[1+sqrt2]`