Two infinitely long straight parallel wires are $$5$$ m apart, perpendicular to the plane of paper. One of the wires, as it passes perpendicular to the plane of paper, intersects it at A and carries current i in the downward direction. The other wire intersects the plane A of paper at point B and carries current i in the outward direction O in the plane of paper as shown in figure. With x and y axes as shown, magnetic induction at O in the component form can be expressed as

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Infinity Learn · Accepted Answer

From trigonometry AP $$=$$ $$16/5$$ and PB $$-$$ $$915$$. Thus,$$sin$$ AOP $$-$$ $$4/5$$ and, $$cos$$ AOP $$-$$ $$3/5$$ $$sin$$ BOP $$=$$ $$3/5$$ and $$cos$$ BOP $$-$$ $$4/5$$ Magnetic field due to A is $$BA=$$μ$$0i8$$π which makes angle θ with  negative $$x-axis$$ and lies in third quadrant.  Magnetic field at O due to wire B is $$BB=$$μ$$0i6$$π which makes   angle θ with $$y-axis$$ and lies in second quadrant.  In component form BA→$$=$$μ$$0i8$$π$$-45i-35j$$ BB→$$=$$μ$$0i6$$π$$-35i+45j$$  Thus, BA→$$+BB$$→$$=$$μ$$0i5$$π$$-i+724j$$

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