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A pair of stationary and infintely long ...

A pair of stationary and infintely long bent wires are placed in the ` XY` planes as shown in fig. The wires carry currents of ` I = 10 amperes` each as shown . 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`.

Text Solution

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The correct Answer is:
A, C, D
:. Magnetic field due to current carrying conductor `P` at point O` is
` B_(1) = (mu_(0))/(4 pi) (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.
` B_(2) = (mu_(0))/( 4pi) (i)/(OS)`
Magnetic field due to current carrying conductors `L and M` at `O` is zero.
:. Resultant magnetic field at `O`
` B = B_(1) + B_(2)`
( directed towards the reader perpendicular to the plane of paper)
rArr B = (mu_(0))/(4 pi) (i)/(OR)+ (mu_(0))/( 4 pi) (i)/(OS) = (mu_(0))/( 4 pi) i [ (1)/(OR) + (1)/(OS) ]`
` = 10^(-7)xx10xx[(1)/(0.02) + (1)/(0.02)] = 10^(-4) tesla`.
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