Question

The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 10²⁸ m⁻³. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10⁻⁶ m² and it is carrying a current of 3.0 A.

Answer 1

Number density of free electrons in a copper conductor, n = 8.5 × 10²⁸ m⁻³

Length of the copper wire, l = 3.0 m

Area of cross-section of the wire, A = 2.0 × 10⁻⁶ m²

Current carried by the wire, I = 3.0 A, which is given by the relation,

I = nAeV_d

Where,

e = Electric charge = 1.6 × 10⁻¹⁹ C

V_d = Drift velocity =`"Length of the wire (l)"/"Time taken to cover l(t)"`

I = `"nAe""l"/"t"`

t = `"nAel"/"I"`

= `(3 xx 8.5 xx 10^28 xx 2 xx 10^-6 xx 1.6 xx 10^-19)/3.0`

= 2.7 × 10⁴ s

Therefore, the time taken by an electron to drift from one end of the wire to the other is 2.7 × 10⁴ s.