Magnetic fields due to currents help

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SUMMARY

The discussion focuses on calculating the net magnetic field at the center of a square formed by four long straight wires carrying currents of 19 A. Wires 1 and 4 have currents flowing out of the page, while wires 2 and 3 have currents flowing into the page. The confusion arises from the diagram's representation of the magnetic field vectors, where it is clarified that B2 and B4 have the same angle, as do B1 and B3. Proper application of the right-hand rule is essential for determining the direction of the magnetic fields.

PREREQUISITES
  • Understanding of Ampère's Law
  • Familiarity with the right-hand rule for magnetic fields
  • Basic knowledge of vector addition
  • Concept of magnetic fields generated by current-carrying wires
NEXT STEPS
  • Study the application of Ampère's Law in different configurations of current-carrying wires
  • Learn about vector addition in the context of magnetic fields
  • Explore the right-hand rule in greater detail with various examples
  • Investigate the effects of multiple current-carrying wires on magnetic field strength and direction
USEFUL FOR

Physics students, electrical engineers, and anyone studying electromagnetism or working with magnetic fields generated by currents.

Nyasha
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Homework Statement



In the figure 29-49, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 20 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 19 A. What is the magnitude of the net magnetic field at the square's center?


http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c29/fig29_45.gif




Solution


I don't understand how they got the diagram with the directions of b1,b2,b3 and b4

200710256626332888916287800006317.jpg
 
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Nyasha said:
I don't understand how they got the diagram with the directions of b1,b2,b3 and b4

There are a couple of confusing things about the picture in the solution:

Firstly, Each vector seems to be going out on its own angle. This is not true, the drawing is not to scale. Treat both B2 and B4 having the same angle, and B1 and B3 having the same angle. I guess the artist is simply trying to make it clear that there are 4 separate vectors, even though two of them are identical, and another two of them are identical.

Secondly, Ignore the +1, -2, -3, and 4 in the corners of the square. I don't know what those are about. They don't match up with the original wires labeled 1, 2, 3, and 4 at all. So when you are trying to figure out which wire goes with which B, look at the figure in the problem statement to get the correct wire number.

If you adhere to the above, the directions fit with the right hand rule.
 

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