Current I is flowing through a copper wire of radius r with drift velocity of electorns `v_(d)`. If this current is passed through another copper wire of same length and double the raduis, what will be the drift velocity of free electrons in it?
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Drift velocity `v_(d)` of the electorns for the current I flowing through a conductor of area of cross-section A, having number density of electrons n and charge on electron e is given by `I=n A e v_(d)` or `v_(d)=(I)/(n Ae) = I/(n(pi r^(2))e)` Where r is the radius of the wire. Thus, `v_(d) prop 1/r^(2)` (since I, n and e are same for another wire) `:. v'_(d)/v_(d) = r^(2)/(2 r)^(2) = 1/4` or `v'_(d) = v_(d)/4` Thus drift velocity of electrons in another wire will become one-fourth of the original value.
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