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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.
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10−7 m2 carrying a current of 1.5 A. Assume the density of conduction electrons to be 9 × 1028 m−3
A conductor of length ‘l’ is connected to a dc source of potential ‘V’. If the length of the conductor is tripled by gradually stretching it, keeping ‘V’ constant, how will (i) drift speed of electrons and (ii) resistance of the conductor be affected? Justify your answer.
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?
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Thomson Effect is caused _______________ .
At room temperature, copper has free electron density of 8.4 × 1028 per m3. The copper conductor has a cross-section of l0−6 m2 and carries a current of 5.4 A. The electron drift velocity in copper is:
The drift velocity of a free electron inside a conductor is ______
- Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
- Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = (1mm)2
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.
