Calculate the B field inside and outside a wire

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SUMMARY

The discussion focuses on calculating the magnetic field (B) inside and outside a long, straight wire with a specific current density defined as J = J0e−β(α−ρ)uz, where β is a constant and ρ < α. The participants clarify that to find B, one must first determine the total current (I) by integrating the current density (J) over the wire's cross-sectional area. The relevant equations include J = I/((π)a^2) and B = (μIρ)/(2(π)(a)^2), which are essential for solving the problem accurately.

PREREQUISITES
  • Understanding of magnetic fields and current density concepts
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of the Biot-Savart Law and Ampère's Law
  • Basic principles of electromagnetism, particularly in cylindrical coordinates
NEXT STEPS
  • Study the derivation of the Biot-Savart Law for magnetic fields
  • Learn about the integration of current density in cylindrical coordinates
  • Explore the implications of boundary conditions on magnetic fields
  • Investigate the effects of varying current densities on magnetic field calculations
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone involved in electromagnetism, particularly those working with current-carrying conductors and magnetic field calculations.

DODGEVIPER13
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Homework Statement


A long, straight wire of radius a has current density J = J0e−β(α−ρ)uz where β is a
constant and ρ < α. Determine B inside and outside the wire.

Homework Equations


J=I/((pi)a^2)
B=(μIρ)/(2(pi)(a)^2)

The Attempt at a Solution


Here is what I did B=(μρ/2)J0e^(-β(alpha-ρ))
 
Last edited:
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Is the problem confusing?
 
DODGEVIPER13 said:
Is the problem confusing?

Not at all. First find i by integrating J then find B. di = JdA
 
So ∫J0e^-β(α-ρ) from 0 to a but what should I integrate with respect too?
 
J=di/dA maybe?
 
well since beta is constant and alpha is greater than rho then e^(-beta(alpha-rho)) whould go to 0 if I took the limit from 0 to infinty
 
hmmm well I guess the problem does not consider time as it uses J0 which I assume stands for the intial value
 
So my limit I idea is flawed then
 
Anything else?
 

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