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Figure shows a long straight wire of a circular cross-section (radius ) carrying steady current . The current is uniformly distributed across this cross-section. Calculate the magnetic field in the region and .
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(a) Consider the case . The Amperian loop, labelled 2 , is a circle concentric with the cross-section. For this loop,
Current enclosed by the loop
The result is the familiar expression for a long straight wire
(b) Consider the case . The Amperian loop is a circle labelled
For this loop, taking the radius of the circle to be ,
Now the current enclosed is not , but is less than this value. Since the current distribution is uniform, the current enclosed is,
Using Ampere's law,
Figure shows a plot of the magnitude of with distance from the centre of the wire. The direction of the field is tangential to the respective circular loop (1 or 2 ) and given by the right-hand rule described earlier in this section.
This example possesses the required symmetry so that Ampere's law can be applied readily.
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Question Text | Figure shows a long straight wire of a circular cross-section (radius ) carrying steady current . The current is uniformly distributed across this cross-section. Calculate the magnetic field in the region and .
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Updated On | Oct 13, 2023 |
Topic | Moving Charges and Magnetism |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 Video solution: 3 |
Upvotes | 462 |
Avg. Video Duration | 3 min |