The point of this problem is to show how slowly electrons travel on average thro

Question

The point of this problem is to show how slowly electrons travel on average through a thin wire, even for large values of current.

A) A wire made from zinc with a cross-section of diameter 0.940 mm carries a current of 12.0 A. Calculate the "areal current density"; in other words, how many electrons per square meter per second flow through this wire?

B)The density of zinc is 7.15 g/cm3, and its atomic mass is 65.3. Assuming each zinc atom contributes two mobile electrons to the metal, what is the number density of free charges in the wire, in electrons/m3?

C) Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire.

D) Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.12×105 m/s, even without any current. What fraction is the current's drift speed, compared to the random thermal motion?

Explanation / Answer

A ;

I = J . A ;

J = I / A ;

J = 12 / ( * ( 0.940/2 e -3 ) ^2 ) ;

J = 1.7291 e 7 C / m^2 ;

no 0f electrons = 1.7291 e 7 / ( 1.6 e -19 ) = 1.080726 e 26 <-----ans

B .

we have to calculte no of free electrons per m^3 ;

no of moles = 7.15 / 65.3 = 0.1094946 ,

no of electrons = 2 * 6.022 e 23 * 0.1094946 = 1.3187 84 e 23 electrons / cm^3 ;

no of electons per m^3 = 1.3187 e 23 / [ (1e-2 )^3 m^3 ] = 1.318784 e 29 per m^3 <----ans

C .

I = n e vd A ;

I = ( 1.318784 e 29 ) ( 1.6 e -19 ) vd * ( * ( 0.940/2 e -3 ) ^2 ) ;

vd = 8.194 e -4 m / s = 0.8194 e -3 m /s ; <---ans

D .

fraction = 0.8194 e -3 / [ 1.12e5 ] = 7.316 e -9 <-------ans

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