LaTeX (i)Show that the magnetic field [latex]\mathbf{B}[/latex] on the axis

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The discussion focuses on deriving the magnetic field on the axis of a circular current loop and a rotating charged disc. The magnetic field for the circular loop is established as B = (μ₀ I a²)/(2(a² + z²)^(3/2)) in the z-direction. Participants explore the surface current density for the rotating disc, leading to an integral for the magnetic field, but face challenges in evaluating it due to the complexity introduced by the r³ term. Suggestions for solving the integral include using substitutions and integration by parts, with a focus on simplifying the expression for limits as z approaches infinity. The conversation also touches on calculating the field for a spinning ring with inner and outer radii, emphasizing the importance of careful manipulation of terms to recover the original magnetic field expression.
  • #31


Substitute that in your original expression and see. Incidentally you won't get back the original term ( the first expression you wrote) but the modified term for z tending to infinity. This is because you've calculated the field using that condition.
 
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  • #32


B(z)=\frac{1}{2} \mu_0 \sigma \omega \frac{r^3 dr}{z^3} as b-> a dr->0 though?
 
  • #33


That's what you should get.
 
  • #34


hmmm...surely if dr->0, then B(z)->0 which doesn't make much sense though?
 
  • #35


You should try to work out an expression for the current through this ring.
 

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