Question

When no current is passed through a conductor

• A. the free electrons do not move
• B. the average speed of a free-electron over a large period of time is zero
• C. the average velocity of a free electron over a large period of time is zero
• D. the average of the velocities of all the free electrons at an instant is zero

Answer 1

Answer: (C), (D)

the average of the velocities of all the free electrons at an instant is zero

The explanation for the correct options (C) and (D):

1. Each electron proceeds along a straight path at constant speeds and collides with the lattice ions when there is no current flowing through the conductor, or when there is no electric field applied to the conductor (positive).
2. The orientation of the electrons changes randomly with each interaction.
3. Any electron's final journey over a lengthy period of time, which includes many collisions, is a random pattern of straight segments.
4. As a result, almost equal numbers of electrons on average pass any small area (in any direction).
5. As a result, over any extended length of time, the average displacement of electrons in any direction is also zero.
6. The average velocity component, then, is 0 in all directions.

In the case of option C,

1. The electrons move randomly in any direction when there is no electric field present.
2. An electron's net displacement is zero.
3. The electron's total velocities during motion add up to zero.
4. The average or net velocity of one free electron will decrease to zero over a long period of time.

In the case of option D,

1. Since the average velocity of a free electron is zero, the total average velocity of all electrons will also be zero.
2. Therefore, the average electron velocity will be zero.
3. Another way to look at this is to consider that since there is no current flowing through the conductor, the net displacement of all the electrons must be zero.
4. This implies that their drift velocity will be zero.
5. Therefore, the average velocities of all the free electrons will always be zero.

The explanation for the incorrect options (A) and (B):

1. In the case of option A, due to the conductor's thermal energy, which stimulates the free electrons, they move even when no current is flowing through them.
2. In the case of option B, since speed is a scalar variable and does not cancel out even after all the random motions, the average speed of an electron will not be zero.

Therefore options C and D are correct.