Find the density rho of mobile charges in a piece of speaker wire made of gold,

Question

Find the density rho of mobile charges in a piece of speaker wire made of gold, assuming each atom contributes one conduction electron. (Look up any necessary physical constants.) Think about the definition of current and then estimate the average electron speed in a gold speaker wire carrying an ordinary current. Your answer will come out quite slow. If you flip on the stereo, and the speakers are, say, 2 meters away, would there be a noticeable "time lag" before you hear the speaker come on? Why/why not? If you cut open this wire, you'll see that it is really two wires, each insulated, and wrapped close together in a single plastic cylinder (since you need a complete circuit, current has to flow TO and FROM the speaker, right?). Make reasonable guesses for the dimensions involved and estimate the size of the magnetic field in the space between the wires. How large a field to you expect at a distance of 1 meter from the pair of wires?

Explanation / Answer

Gold has a density of 19.32 g/cm3, and an atomic weight of 196.96 g/mol, so there are (19.32*10^6/196.96)=1895117.79 mol/m3. In one mole of any element there are 6.02×1023 atoms (Avogadro's constant). Therefore in 1 m3 of copper there are about 1.14*10^(30) atoms (6.02×1023 × 140685.5 mol/m3). Copper has one free electron per atom, so n(eletron density) is equal to 1.14×10^(30) electrons per cubic metre.So charge density=1.83*10^(11) C/m^3.

Yes there will be some time lag (in fractions of seconds) which we will not be able to notice because electroc takes time to travel and so the sound

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