Current is flowing out of the page, through the Amperian loop shown. Consider th

Question

Current is flowing out of the page, through the Amperian loop shown. Consider the following student dialogue: Student 1: "By the right hand rule the magnetic field will point counter-clockwise, so the line integral will be positive." Student 2: "I disagree. The area vector should be into the page which makes the encircled current negative, so the line integral is also negative." Is either student correct? Could both be correct? Explain. A current distribution (not shown) creates the spatially varying magnetic field shown at right. In region I the magnetic field increases in magnitude toward the bottom of the page. In region II the magnetic field is uniform, and in region III the magnetic field is zero. Consider loop a (in region I). Draw and label an area vector for loop a on the diagram.

Explanation / Answer

1) The current given as a dot implies that the current is directed out of the page and so from the right hand rule, pointing thumb out of the page fingers are curled in anti-clockwise direction, Therefore the magnetic field on the dotted circle will be in counter-clockwise sense and so the line integral will be positive. So the first student's argument is correct.

2) Second student argues that the area vectro points into the page which is wrong, becasue area vector can point out of the page or into the page depending on the direction of magnetic field and current.

So only the first student is correct

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