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Are the paths of free electrons straight...

Are the paths of free electrons straight lines between successive collisions (with the positive ions of metal wire) in the-
(i) Absence of electric field (ii) Presence of electric field

A

`sqrt((mv_(0)^(2))/(12k))`

B

`sqrt((mv_(0)^(2))/(5k))`

C

`sqrt((mv_(0)^(2))/(10k))`

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the paths of free electrons in a metal wire under different conditions, we will analyze both scenarios: the absence of an electric field and the presence of an electric field. ### Step-by-Step Solution: **Step 1: Analyze the absence of an electric field.** - In the absence of an electric field, free electrons in a metal wire move randomly due to thermal energy. However, they experience collisions with positive ions (the lattice structure of the metal). - During their motion, the electrons travel in straight lines between these collisions. The random thermal motion does not influence the straight-line path between collisions. **Conclusion for Step 1:** - In the absence of an electric field, the paths of free electrons are straight lines between successive collisions. **Step 2: Analyze the presence of an electric field.** - When an electric field is applied to the metal wire, it exerts a force on the free electrons, causing them to accelerate in the direction opposite to the electric field (since electrons are negatively charged). - Although the electrons may initially move in a straight line due to the electric field, they will still collide with the positive ions of the metal lattice. These collisions will cause the electrons to scatter and change direction. - As a result, the overall path of the electrons will not be a straight line. Instead, it will be influenced by both the electric field and the random nature of the collisions, leading to a more complex trajectory. **Conclusion for Step 2:** - In the presence of an electric field, the paths of free electrons are not straight lines; they are twisted or curved due to the influence of the electric field and collisions. ### Final Conclusion: - (i) In the absence of an electric field, the paths of free electrons are straight lines between successive collisions. - (ii) In the presence of an electric field, the paths of free electrons are not straight lines; they are twisted or curved.
To solve the question regarding the paths of free electrons in a metal wire under different conditions, we will analyze both scenarios: the absence of an electric field and the presence of an electric field. ### Step-by-Step Solution: **Step 1: Analyze the absence of an electric field.** - In the absence of an electric field, free electrons in a metal wire move randomly due to thermal energy. However, they experience collisions with positive ions (the lattice structure of the metal). - During their motion, the electrons travel in straight lines between these collisions. The random thermal motion does not influence the straight-line path between collisions. ...
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Knowledge Check

  • Assertion: Drift velocity of electrons is independent of time. Reason: Electrons are accelerated in the presence of electric field.

    A
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    B
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    D
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