In a certain region there is a uniform current density of in the positive z direction. We have to find the value of when the line integral is taken along three straight-line segments from to to to , where .

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As the line integral is traversed in the counter-clockwise direction, and as the currents enclosed are in the z direction, they will contribute with positive sign in the Ampere’s law. It is given that the current density is uniform and is . From the diagram, we note that as the area enclosed by the Amperian path is that of a triangle with base 3d and height 4d, it is

where the current density