# A pair of stationary and infinitely long bent wires are placed in the XY plane as shown in fig. The wires carry currents of  i = 10 amperes each as shown. The segments L and M are along the X – axis. The segments P and Q are parallel to the Y –axis such that OS = OR = 0.02 m. Find the magnitude and direction of the magnetic induction at the origin O

Navjyot Kalra
9 years ago
Hello Student,
KEY CONCEPT : The magnetic field due to an infinitely long current carrying conductor at one end of the conductor at a distance r is given by
B = μ0 i/ 4π r
∴ Magnetic field by to current carrying conductor P at point O is
B1 = μ0 / 4π I / (OR)
directed towards the reader perpendicular to the plane of paper.
Magnetic field due to current carrying conductor Q at point O is directed towards the reader perpendicular to the plane of paper.
B2 = μ0 / 4π i / (OS)
Magnetic field due to current carrying conductors L and M at O is zero.
∴ Resultant magnetic field at O
B = B1 B2
(directed towards the reader perpendicular to the plane of paper)
⇒ B = μ­0 / 4π I / OR + μ0 / 4π I / OS = μ0­ / 4π I [ 1 / OR + 1 / OS]
= 10-7 x 10 x [1 / 0.02 + 1 / 0.02] = 10-4 tesla.
Thanks
Navjot Kalra