Advertisements
Advertisements
Question
Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence, obtain an expression for it.
Advertisements
Solution
We know that free electrons are the current carriers in a metallic conductor, and these free electrons move randomly in all directions and constantly collide with the positive ions inside the metal, resulting in an average thermal velocity of zero. When an electric field is applied across the two ends of the metallic conductor, an electric field is set up across the two ends of the conductor, and now free electron moves in a particular direction due to external elution.
Expression for drift velocity: When a potential difference is applied across a conductor, an electric field is produced and free electrons are acted upon by an electric force (F = -Ee). Due to this, electrons accelerate and keep colliding with each other and acquire a constant (average) velocity, `v_d`.
∴ F = -Ee = `-(V/l)e`
∴ E = `V/l`
As `a = (-F)/m = (-eV)/(lm)`
and also `v` = u + at
∴ u = 0, t = τ(relaxation time)
`v_d = -atau`
`v_d = (-eV)/(lm)tau`
APPEARS IN
RELATED QUESTIONS
What is its relation with relaxation time?
Write its (‘mobility’ of charge carriers) S.I. unit
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2.5 × 10−7 m2 carrying a current of 1.8 A. Assume the density of conduction electrons to be 9 × 1028 m−3.
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2·5 × 10−7 m2 carrying a current of 2·7 A. Assume the density of conduction electrons to be 9 × 1028 m−3
The number density of free electrons in a copper conductor 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.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
The drift velocity of a free electron inside a conductor is ______
Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?
The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of ρ with temperature. Elaborate why?
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.
