Two infinitely long straight wires lie in the $$xy-plane$$ along the lines $$x=$$±R. The wire located at $$x=+R$$ carries a constant current $$I1$$ and the wire located at $$X=-R$$ carries a constant current $$I2$$ . A circular loop of radius R is suspended with its center at $$0$$,$$0$$,$$3R$$ and in a plane parallel to the $$xy-plane$$. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $$+j^$$ direction. Which of the following statements regarding the magnetic field B→ is (are) true?

Question

Two infinitely long straight wires lie in the $$xy-plane$$ along the lines  $$x=$$±R. The wire located at  $$x=+R$$ carries a constant current  $$I1$$ and the wire located at  $$X=-R$$ carries a constant current  $$I2$$ . A circular loop of radius R is suspended with its center at $$0$$,$$0$$,$$3R$$  and in a plane parallel to the $$xy-plane$$. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $$+j^$$  direction. Which of the following statements regarding the magnetic field B→  is (are) true?

Infinity Learn · Accepted Answer

$$A)At$$ origin ,B→ $$=$$ $$0$$ due to two wires if $$I1=I2$$, hence B→net at origin is equal to B→ due to ring , which is non –zero.$$B)If$$ $$I1$$>$$0$$ and $$I2$$<$$0$$ , B→ at origin due to wires will be along $$+k^$$ direction and B→ due to ring is along $$-k^$$ direction and hence B→ can be zero at origin.$$C)If$$ $$I1$$<$$0$$ and $$I2$$>$$0$$, at origin due to wires will be along $$-k^$$ and B→ due to ring is also along $$-k^$$ , hence B→ cannot be zero .$$D)$$ At center of ring, due to wires B→ is along $$x-axis$$.B→ along z axis is only due to current in ring.∴B→$$=$$−μ$$0I2Rk^$$

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