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stop equation The velocity likely $psi$ obeys the identical differential equation given that the electrostatic prospective in totally free Place ($rho=0$).
Consider the subsequent instance. We would like for a few Unique experimental condition to rearrange the major area of the table could have a really uniform illumination. We have accessible long tubular fluorescent lights which radiate uniformly along their lengths.
) We'll stress only regarding the situation by which the tension $tau$ is consistent all over the sheet. We will then generate for Eq. (12.seventeen), begin equation label Eq:II:12:18 nabla^2u=-frac f tau . close equation We've got An additional equation that's similar to for electrostatics!—only this time, restricted to two-dimensions. The displacement $u$ corresponds to $phi$, and $f/tau$ corresponds to $rho/epsO$. So the many perform We've got completed for infinite airplane charged sheets, or very long parallel wires, or billed cylinders is specifically relevant for the stretched membrane.
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inside of a uniform electric powered industry. If we experienced labored out the solution to the trouble of the sphere of a dielectric constant $kappa$ within a uniform discipline, then by putting $kappa=0$ we'd instantly have the answer to this issue.
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