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प्रश्न
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.
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उत्तर
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`
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संबंधित प्रश्न
Derive an expression for drift velocity of free electrons.
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Derive an expression for resistivity of a conductor in terms of the number density of charge carriers in the conductor and relaxation time.
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.
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