Magnetic Field in a Cylindrical Conductor

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SUMMARY

The discussion focuses on calculating the magnetic field within a cylindrical conductor with a radius of 2.49 cm carrying a current of 2.17 A. Initially, the incorrect formula B = µI / 2πr was applied, leading to an erroneous result. The correct formula for the magnetic field inside the conductor is B = µIr / 2πa², which yielded the accurate magnetic field value of 8.71e-6 T at r = R/2. This highlights the importance of using the appropriate equations for specific scenarios in electromagnetism.

PREREQUISITES
  • Understanding of Ampère's Law
  • Familiarity with the concept of magnetic fields in conductors
  • Knowledge of the permeability of free space (µ)
  • Ability to manipulate equations involving current and radius
NEXT STEPS
  • Study the derivation of Ampère's Law for cylindrical conductors
  • Learn about the applications of the magnetic field in various conductor geometries
  • Explore the concept of magnetic field strength and its dependence on current and geometry
  • Investigate the role of permeability in different materials
USEFUL FOR

Students of electromagnetism, physics educators, and engineers working with electrical conductors will benefit from this discussion, particularly those focusing on magnetic field calculations in cylindrical geometries.

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Homework Statement



A cylindrical conductor of radius R = 2.49 cm carries a current of I = 2.17 A along its length; this current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field midway along the radius of the wire (that is, at r = R/2).

Radius (m) = 2.49 cm = 0.0249 m = 0.01245 m (as asked)
Current (I) = 2.17 A


Homework Equations



I thought it was B = µI / 2πr because i was given a sheet of equations and this was the only one that seemed to fit it.


The Attempt at a Solution



B = µI / 2πr
B = (4π x 10^-7)(2.17) / 2π(0.01245)
B = 3.49e-5 T

Though this isn't the right answer. Not sure what's gone wrong here.
I also thought it was zero since it's a "conductor" also not right...
 
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Not to worry, i got the answer. I was using the wrong equation.
For values of Magnetic Field inside the given radius the equation is

B = µIr / 2πa^2
B = (4π x 10^-7)(2.17)(0.01245) / 2π(0.0249^2)
B = 8.71e-6 T

In case anyone else had the same or similar problems.
 
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