Shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of taken in the directions shown, most positive first.
The ranking of the paths according to the value of , the most positive first is .
Using Ampere’s law, find the values along each path. Comparing them, rank the paths according to the value .
The formula is as follows:
= is the magnetic field,= is the infinitesimal segment of the integration path,
= is the empty's permeability,
= is the enclosed electric current by the path.
According to Ampere’s law,
From the given figure, it can interpret that,
For path (a),
Hence, the path of (a) is .
For path (b),
Hence, the path of (b) is .
For path (c),
Hence, the path of (c) is .
For path (d),
Hence, the path of (d) is .
For path (e),
Hence, the path of (e) is .
Hence, the ranking of the paths according to the value of , the most positive first is .
Ampere’s law gives the relation between magnetic flux and current enclosed by the loop.
The current-carrying wire loop in Fig. 29-60a lies all in one plane and consists of a semicircle of radius , a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angle , until it is perpendicular to the plane (Fig.29-60b). Figure 29-60c gives the magnitude of the net magnetic field at the center of curvature versus angle . The vertical scale is set by . What is the radius of the smaller semicircle?
Figure 29-45 shows two current segments. The lower segment carries a current of and includes a semicircular arc with radius , angle , and center point P. The upper segment carries current and includes a circular arc with radius , angle , and the same center point P. What are the(a) magnitude and (b) direction of the net magnetic field at P for the indicated current directions? What are the (c)magnitude of if i1 is reversed and (d) direction of if i1 is reversed?
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