Chapter 12: Problem 5
Two infinitely long straight wires lie in the \(x y\) -plane along the lines \(x=\pm R\). The wire located at \(x=+R\) carries a constant current \(I_{1}\) and the wire located at \(x=-R\) carries a constant current \(I_{2} .\) A circular loop of radius \(R\) is suspended with its centre at \((0,0, \sqrt{3} R)\) and in a plane parallel to the \(x y\) -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 \(+\hat{\jmath}\) direction. Which of the following statements regarding the magnetic field \(\vec{B}\) is (are) true? (A) If \(I_{1}=I_{2}\), then \(\vec{B}\) cannot be equal to zero at the origin \((0,0,0)\) (B) If \(I_{1}>0\) and \(I_{2}<0\), then \(\vec{B}\) can be equal to zero at the origin \((0,0,0)\) (C) If \(I_{1}<0\) and \(I_{2}>0\), then \(\vec{B}\) can be equal to zero at the origin \((0,0,0)\) (D) If \(I_{1}=I_{2}\), then the \(z\) -component of the magnetic field at the centre of the loop is \(\left(-\frac{\mu_{0} I}{2 R}\right)\)
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