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Question

The figure shows a cross -section of along thin ribbon of width b that is carrying a uniformly disturbed total current i into the page. Calculate the magnitude and direction of the magnetic field B at a point P in the plane of the ribbon at a distance afrom its edge.


A


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B


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C


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D

Zero

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Solution

The correct option is C



Take a small element of thickness dx at a distance x from P. The current in the element is di=ibdx,

and magnetic at P, dB=μ02πdix=μ02π(ib)dxx
The total field B=μ02πib(a+b)adxs=μ02πib|lnx|(a+b)a=μ02πib In (a+b)a


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