A pair of stationary and infinitely long bent wires is placed in he xy plane as shown in figure. Each wire carries current of $$10$$ A. Segments L and M are along the $$x-axis$$. 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 origin ‘O’

Question

A pair of stationary and infinitely long bent wires is placed in he xy plane as shown in figure. Each wire carries current of $$10$$ A. Segments L and M are along the $$x-axis$$. 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 origin ‘O’

Infinity Learn · Accepted Answer

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. ⇒ $$BR=$$μ$$04$$$$π$$$$IRO+$$μ$$04$$$$π$$ISOBut  $$RO=SO=0.02MHence$$, $$BR=2$$×μ$$04$$π×$$100.02=2$$×$$10$$−$$7$$×$$100.02=10$$−$$4$$ T .

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