- #1
malindenmoyer
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Two very large parallel conducting plates of very large length l, and width w are separated by a distance d. A current I=Jw flows to the right in the lower plate and to the left in the upper plate. Each of the two currents produces a magnetic field \frac{B}{2} between the two plates.
(a) Show that the total field between the plates is B=\mu_0 J via Ampere's Circuital Law.
(b) Find the flux \phi and the self inductance per unit lenght, \frac{L}{l} for this arrangement.
(c) Find the capacitance per unit length, \frac{C}{l}.
(d) Find \sqrt{\frac{L}{C}} in terms of \mu_0, \epsilon_0 and geometrical factors
My Attempt at Solution
Part (a) is confusing as I have not used the circuital Law for rectangular geometry. I know that Ampere's Law is given by:
\oint_C \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} = \mu_0 I_{\mathrm{enc}}
But am confused as to how to apply it as it is not circular geometry.
In part (b) I know that:
\phi=BA
But am not sure as to what area to use, since we know B per part (a)
Solving for flux leads us one step closer to finding the self inductance which is:
L=\frac{N\phi}{I}
But again, I do not know what value to substitute in for N.
I am pretty sure I can find the capacitance per unit length per (c), and then (d) is a matter of combing (b) and (c) so that would be self explanatory. Could somebody help me get this thing started? Please keep in mind that I have a very elementary understanding of this material.
Thanks.
(a) Show that the total field between the plates is B=\mu_0 J via Ampere's Circuital Law.
(b) Find the flux \phi and the self inductance per unit lenght, \frac{L}{l} for this arrangement.
(c) Find the capacitance per unit length, \frac{C}{l}.
(d) Find \sqrt{\frac{L}{C}} in terms of \mu_0, \epsilon_0 and geometrical factors
My Attempt at Solution
Part (a) is confusing as I have not used the circuital Law for rectangular geometry. I know that Ampere's Law is given by:
\oint_C \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} = \mu_0 I_{\mathrm{enc}}
But am confused as to how to apply it as it is not circular geometry.
In part (b) I know that:
\phi=BA
But am not sure as to what area to use, since we know B per part (a)
Solving for flux leads us one step closer to finding the self inductance which is:
L=\frac{N\phi}{I}
But again, I do not know what value to substitute in for N.
I am pretty sure I can find the capacitance per unit length per (c), and then (d) is a matter of combing (b) and (c) so that would be self explanatory. Could somebody help me get this thing started? Please keep in mind that I have a very elementary understanding of this material.
Thanks.