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Q.

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in fig. The wires carry a current I=10A each as shown

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The segments LR and SM are along the x-axis. The segments PR and QS are along the y-axis, such that OS=OR=0.02m. What is the magnitude and direction of the magnetic field at the origin O?

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a

 104  Wbm2 vertically downward

b

 104  Wbm2 vertically upward

c

100  Wbm2 vertically upward

d

102  Wbm2 vertically downward

answer is C.

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Detailed Solution

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As point ‘O’ is along the length of segments ‘L’ and M, so the field at ‘O’ due to these segments will 
be zero. Also point ‘O’ is near one end of along wire.
The resultant field at ‘O’.  BR=BP+BQ. This field due to both P and Q will be into the plane of paper, hence will add up.
 BR=μ04πIRO+μ04πISO
But  RO=SO=0.02M
Hence, BR=2×μ04π×100.02=2×107×100.02=104 T .

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