EM waves in highly conducting can be described with the following differential equation: ?x2?2E(x,t)?=????t?E(x,t)? vhere ? and ? are constants that depend on the material. a. Show that E=E0?e?kC?xei(kC?x??t) is a solution to this equation with kC2?=2???? b. Assume ?=?0?,?=1.7210?8??m and f=2.0MHz.. Find the distance at which the electric field solutionspile.com

Question

EM waves in highly conducting can be described with the following differential equation:

\frac{? ^{2} E ( x , t )}{? x ^{2}} = \frac{?}{?} \frac{? E ( x , t )}{? t}

vhere

?

and

?

are constants that depend on the material. a. Show that

E = E_{0} e^{? k_{C} x} e^{i (k_{C} x ? ? t)}

is a solution to this equation with

k_{C}^{2} = \frac{? ?}{2 ?}

b. Assume

? = ?_{0}, ? = 1.72 \times 1 0^{? 8} ? ? m

and

f = 2.0 MHz

.. Find the distance at which the electric field amplitude drops by a factor of 2. Hint1: consider only

E_{0} e^{? k_{c} x}

. Hint2 all units given here are mks except for

MHz

, which you should convert.

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