Answer to Question #166555 in Electricity and Magnetism for JayJay

Question

Suppose the telephone line linking America and London is a copper wire of length 6000km.if the current is 0.6mA, what is the drift velocity of electrons in the wire? if telephone impulses were to travel at this speed, how long would it take to transmit a message along the line? Estimate the actual time taken. The diameter of the wire is 5 x 10-4m, the number density of copper atoms is 8.4 x 1028 and the speed of em is 3 x 108ms-1

Answer 1

(a) By the definition of the drift velocity, we get:

$$v_{drift}=\dfrac{I}{nAq},$$ $$v_{drift}=\dfrac{0.6\cdot10^{-3}\ A}{8.4\cdot10^{28}\ m^{-3}\cdot\dfrac{\pi\cdot(5\cdot10^{-4}\ m)^2}{4}\cdot1.6\cdot10^{-19}\ C}=2.27\cdot10^{-7}\ \dfrac{m}{s}.$$

b)  If telephone impulses were to travel at this speed, the time taken to transmit a message along the line equals:

$$t=\dfrac{d}{v}=\dfrac{6\cdot10^6\ m}{2.27\cdot10^{-7}\ \dfrac{m}{s}}=2.64\cdot10^{12}\ s=83814\ yr.$$

c) Let's estimate the  actual time taken:

$$t=\dfrac{d}{v}=\dfrac{6\cdot10^6\ m}{3\cdot10^8\ \dfrac{m}{s}}=0.02\ s.$$