The number density of free electrons in a copper conductorestimated in Example 3.1 is 8.5 × 1028 m–3. How long does an electrontake to drift from one end of a wire 3.0 m long to its other end? Thearea of cross-section of the wire is 2.0 × 10–6 m2 and it is carrying acurrent of 3.0 A.
Given: The number density of free electrons in a copper conductor 8.5 × 10 28 m -3 , the length of copper wire is 3.0 m , the area of cross section of the wire, 2 .0 × 10 − 6 m 2 , the Current is 3.0 A .
The current is given as,
I = n e A l t
Where, the current carried by wire is I , the number density of free electrons is n , the length of the copper wire is l , the cross-section area of wire is A , the charge of electron is e and the time taken to cover the length is t .
By substituting the given values in the above formula, we get
3.0 = 8.5 × 10 28 × 2 × 10 − 6 × 1.6 × 10 − 19 × 3 t t = 8.5 × 10 28 × 2 × 10 − 6 × 1.6 × 10 − 19 × 3 3 t = 2.7 × 10 4 s
Thus, an electron drifts from one end of the wire to other end in 2.7 × 10 4 s .
Given: The number density of free electrons in a copper conductor
The current is given as,
Where, the current carried by wire is
By substituting the given values in the above formula, we get
Thus, an electron drifts from one end of the wire to other end in
