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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
Define the term drift velocity.
Write its (‘mobility’ of charge carriers) S.I. unit
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.
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Why alloys like constantan and manganin are used for making standard resistors?
When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?
When a current is established in a wire, the free electrons drift in the direction opposite to the current. Does the number of free electrons in the wire continuously decrease?
Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in A is 1.5 times that in B. Find the ratio of the drift velocity of electrons in wire A to that in wire B.
The drift velocity of electrons in a conductor connected to a battery is given by vd = `(−"eE" τ)/"m"`. Here, e is the charge of the electron, E is the electric field, τ is the average time between collisions and m is the mass of the electron.
Based on this, answer the following:
- How does the drift velocity change with a change in the potential difference across the conductor?
- A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.
