Magnetic Field in a Semi-Infinite Wire

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SUMMARY

The discussion centers on calculating the magnetic field (B) around a semi-infinite wire using the formula B = μi / 4πR. Participants express confusion about determining the appropriate value for R in various scenarios. It is clarified that the formula applies only to points in a plane perpendicular to the wire and located at its end. Understanding the derivation of the formula and the significance of the radius (r) in relation to the current is essential for solving the problem accurately.

PREREQUISITES
  • Understanding of magnetic fields and their calculations
  • Familiarity with the Biot-Savart Law
  • Knowledge of cylindrical coordinates
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of the Biot-Savart Law
  • Learn about magnetic field calculations for infinite and semi-infinite wires
  • Explore the application of cylindrical coordinates in electromagnetism
  • Investigate the effects of current distribution on magnetic fields
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching magnetic field concepts, and anyone involved in solving problems related to magnetic fields around current-carrying wires.

Adeel Ahmad
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Homework Statement


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Homework Equations


B = μi / 4πR is the equation for a semi-infinite straight wire

The Attempt at a Solution


I know that for each situation in a,b, and c I would use the equation I listed above, but I am not sure what I would plug in for R for each situation.
 
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Can someone help out please
 
Thanks, but I know which equations to use, I just don't know how to apply them. I don't know what to plug in for r in each situation.
 
The problem is not clear concerning the location of the points where you are to find B. For a fixed value of r, the field will vary as you move parallel to the axis of the cylinder. I guess you are to assume that you are looking for B only at points in a plane that is perpendicular to the axis and located at the end of the cylinder.

Likewise, the formula you gave for a semi-infinite wire is only valid for points in a plane oriented perpendicular to the wire and located at the end of the wire.

To work this problem you need to understand how to obtain the formula you gave for the semi-infinite wire. The same reasoning can be used to help solve the cylinder problem.
 
Adeel Ahmad said:
Thanks, but I know which equations to use, I just don't know how to apply them. I don't know what to plug in for r in each situation.
The text at that link does answer your question. In brief, it is only the currents inside the selected radius r that matter. For r<b, what is the current inside?
 

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