Electrical current does not always flow through copper wires. Current is defined

Question

Electrical current does not always flow through copper wires. Current is defined as the amount of charge passing through an area per unit time. Us this fundamental definition to determine the current in the following situations. (a) Synchrotron radiation is emitted by charged particles traveling at relativistic speeds and is used to study the structure of molecules, crystals, and proteins. In a 6 GeV electron synchrotron, electrons travel around in a circular path 240m long. It is normal to have about 10^11 electrons circulating when the machine is in operation. The speed of the electrons is nearly the speed of light. What is the current of the electron beam? (b) If 3.0 g of gold is deposited on the negative elecrode of an electrolytic cell during a period of 3 hours, what is the current through the cell during this period? Assume the gold ions carry one elementary unit of positive charge.

Explanation / Answer

The relation between current and charge is

I = Q/t

but Q= ne

I = ne/t

the relation between distance and time is

t = d/v

I = ne/ d/v

= nev/d

= 10^11 ( 1.6 * 10^-19) ( 3* 10^8)/240 m = 0.02 A or 20 mA

(b)

mass of single gold atom is

m = M/N = 197 g/mol/6.023 * 10^23 = 3.27 * 10^-25 kg

number of atoms deposited on the negative electrode is

n= z/m = 3* 10^-3 kg/3.27 * 10^-25 = 9.17 * 10^21

I = ne/t = 9.17 * 10^21 ( 1.6 * 10^-19)/3( 3600 s) = 0.135 A

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