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A copper wire has a square cross section...

A copper wire has a square cross section of 6 mm on a side. The wire is 10 m long and carries a current of 3.6A. The density of free electrons id `8.5x10^(28)//m^3.`Find the magnitude of (a) the current density in the wire , (b) the electric field in the wire. (c ) How much time is required for an electron to travel the length of the wire? `("rh, electrical resistivity, is" 1.72 xx10^(-8) Omegam.)`

Text Solution

Verified by Experts

Given ` r= 6 mm, I = 10 m, I = 3.6 A, n = 8.5xx10^(28)//m^3`
(a) To find the currrent density, formula used should be
`J=I//A =(3.6)/((6xx10^(-3))^(2))=(3.6)/(36xx10^(-6))=10^(5) Am^(-2)`
(b) Electric field is
`E = rhoJ = 1.72xx10^(-8) xx10^5 = 1.72 xx10^(-3)Vm^(-1)`
(c ) Time taken is
`t = (I)/(v_d) = (I"ne"A)/(I)`
`=(10xx8.5xx10^(28)xx1.6xx10^(-19)xx(6xx10^(-3))^(2))/(3.6)`
`=1.36xx10^6 s`
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