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An Eddy Current brake: Check my answer?

  • Thread starter AJKing
  • Start date
103
2
1. Homework Statement

Refer to Figure attached.

A disk of conductivity σ and thickness b rotates around an axis through its center with a magnetic field B applied perpendicular to the plane of the disk over a small area a2. Find the approximate torque tending to slow the disk at the instant its angular velocity is ω.

2. Homework Equations
3. The Attempt at a Solution

[itex]\xi = -B \frac{dA}{dt} [/itex]

[itex] = -B a \frac{da}{dt} [/itex]

(Right here ^ Can I do this?)

[itex] = -B a v [/itex]

[itex] = -B a \omega dr [/itex]

[itex] \Rightarrow \int^{r+a/2}_{r-a/2} -B a \omega dr [/itex]

[itex] = - B a^2 \omega [/itex]

And

[itex] R = \frac{L}{\sigma A} = \frac{a}{\sigma ab} = \frac{1}{\sigma b}[/itex]

-----
-----

Thus

[itex]F = i a \times B[/itex]

[itex] = \frac{\xi}{R} a \times B[/itex]

[itex] F = - B^2 a^2 \omega \sigma b [/itex]

-----
-----

[itex]\tau = \int F dr[/itex]

[itex]\tau = - B^2 a^2 \omega \sigma b \int^{r+a/2}_{r-a/2} dr[/itex]

[itex]\tau = - B^2 a^3 \omega \sigma b[/itex]
 

Attachments

Last edited:
103
2
I think I've handled my integrals poorly...
will revise.
 

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