Calculate the B field inside and outside a wire

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Discussion Overview

The discussion revolves around calculating the magnetic field (B field) inside and outside a long, straight wire with a specific current density profile. Participants explore the mathematical approach to solving the problem, including integration techniques and the implications of constants in the equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the initial attempt at a solution for B using the given current density and equations.
  • Another participant suggests that the problem may be confusing and prompts for clarification.
  • A different participant advises to first find the current (i) by integrating the current density (J) over the area.
  • There is a question about the limits of integration, specifically what variable to integrate with respect to when calculating the current.
  • One participant proposes that J could be expressed as the differential of current with respect to area.
  • Another participant notes that since beta is constant and alpha is greater than rho, the exponential term approaches zero when considering limits from zero to infinity.
  • There is speculation about the implications of using J0, suggesting it may represent an initial value, which leads to a reconsideration of the limit idea.
  • A participant expresses uncertainty about the validity of their limit approach.
  • The thread concludes with a request for any additional thoughts or insights on the problem.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the approach to solving the problem, as there are multiple perspectives on the integration process and the interpretation of constants involved.

Contextual Notes

Participants express uncertainty regarding the limits of integration and the assumptions about the constants in the problem, indicating potential gaps in understanding the problem's setup.

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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