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Question

A pair of stationary and infinitely long bent wires is placed in the x-y plane as shown in figure. Each wire carries current of 10A. Segments L and M are along the x-axis.Segments P and Q are parallel to the y-axis such that OS=OR=0.02m. Find the magnitude and direction of the magnetic induction at origin O in the form of x×104. What is x.
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Solution

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 a long wire.
The resultant field at O, BR=BP+BQ, this field willbe into the plane paper.
BR=μ04πIRO+μ04πISO
But, RO=SO=0.02m
Hence, BR=2×μ04π×100.02=2×107100.02=104Wb m2

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