Magnitude of magnetic field at distance from central axis

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SUMMARY

The discussion focuses on calculating the magnitude of the magnetic field at specific distances from a coaxial cable consisting of an inner conductor with a radius of 0.040 m carrying a current of 4.4 A and an outer conductor with inner and outer radii of 0.080 m and 0.090 m, respectively, carrying a current of 6.9 A in the opposite direction. The magnetic field is calculated using the formula B = (μ0 * I * r) / (2π * a^2) for cylindrical conductors. The two specified distances for calculation are 0.060 m (within the gap) and 0.150 m (outside the cable). The permeability constant μ0 is given as 4π × 10^-7 T·m/A.

PREREQUISITES
  • Understanding of magnetic fields in cylindrical conductors
  • Familiarity with Ampère's Law
  • Knowledge of the permeability of free space (μ0)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the application of Ampère's Law in cylindrical geometries
  • Learn about the magnetic field calculations for coaxial cables
  • Explore the implications of current direction on magnetic field strength
  • Investigate the effects of varying distances from conductors on magnetic field intensity
USEFUL FOR

Students studying electromagnetism, electrical engineers, and anyone involved in the design or analysis of coaxial cable systems.

qlzlahs
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Homework Statement


A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R2 = 0.080 m and outer radius R3 = 0.090 m. The inner conductor carries current I1 = 4.4 A in one direction, and the outer conductor carries current I2 = 6.9 A in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable?
(μ0 = 4π × 10-7 T · m/A)
(A) At r = 0.060 m (in the gap midway between the two conductors)
(B) At r = 0.150 m (outside the cable)

Homework Equations


1. B = (μ_0/(4pi))*(Q)*(v x r)/(r^2)
2. B = ((μ_0/(2pi))*(I)*(r^2 / R^3)

The Attempt at a Solution


I'm just really not sure how to solve this. Do I plug this in the 1st equation or the second? What is r (and R)? Is there a different equation I can use?
 
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qlzlahs said:
Do I plug this in the 1st equation or the second?
This right here is your problem. Physics is not about finding a formula to plug things in to. In order to learn you need to understand in which situations your formulae are applicable. So what do the formulae you quoted eescribe?
 
Orodruin said:
In order to learn you need to understand in which situations your formulae are applicable

Whoops. So I think I use this equation for magnetic fields in cylindrical conductors?:
B = (µ_0*I*r) / (2π*a^2), where a is the radius and r is the distance.
 

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