Having trouble with the 3rd question. What formula was used and if you state the

Question

Having trouble with the 3rd question. What formula was used and if you state the formula, please also explain what each symbol represents. Show all works and explaination. Thanks =D

The displacement of a circular drumhead of radius a is described by the wave equation in 2D polar coordinates Look for axisymmetric solutions (independent of theta that are also sinusoidal in time: u(r, theta, t) = R (r) e-iwt. Plug this assumed solution into the wave equation to derive a differential equation for R (r). What are the boundary conditions to be used in the differential equation for R you derived in part (a)? What are the solutions to the resulting boundary value problem? You should find that axisymmetric, sinusoidal-in-time solutions exist only for specific frequencies omega. What is the lowest frequency omega at which axisymmetric, sinusoidal-in-time oscillations can occur?

Explanation / Answer

Given Data

diameter = 0.55 mm => Radius = 0.275 mm = 0.275*10^-3 m

current , I = 2.5 x 10-6A

We have

Density of free mobile electron for copper, n = 8.4 e 28 m-3

Charge of Electron, e = 1.60 x 10-19C

resistivity of copper = 1.68 x 10-8 Ohm-m

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a) To Find

drift speed, vd = ?

I = neAvd

I = ne(pr2)vd;

2.5 x 10-6A = (8.4 x 1028m-3)(1.60 x 10-19C)[p(0.275 x10-3m)2]vd,

vd = 7.83*10^-10 m/s

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b) To Find

current density , j = ?

j = I/A

= 2.5 x 10-6A / [p(0.275 x10-3m)2]

j = 10.52 A/m^2

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c) To Find

electric field , E = ?

j = E/r;

E = j*r

    = 10.52*1.68 x 10-8

E = 1.767 *10^-7 V/m

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