Work done by uniform electric field and potential in conductors

[metz143]

Question. Anyone dare to answer?

Question1: A uniform electric field is parallel to the x-axis. Inwhat direction can a charge be displace in this field without any external work being done on the charge?

Question2: Why is it that under static conditions, all points in a conductor must be at the same electric potential?

Happy answering & happy new year!

 

[Andrew Mason]

Question1: A uniform electric field is parallel to the x-axis. Inwhat direction can a charge be displace in this field without any external work being done on the charge?

The definition of work is $W = \vec F \cdot \vec d = qE cos\theta d$. So if no work is done, the displacement must be in the direction perpendicular to the force ie $cos\theta = 0 \rightarrow \theta = \pi/2$

Question2: Why is it that under static conditions, all points in a conductor must be at the same electric potential?

In a conductor, the population of free electrons are free to move. So a free electron will move if there is an electric potential difference between it and another charge. So if there is no motion, there can be no potential difference between charges.

AM

 

[wais]

1) A charge can be displaced in any direction parallel to the electric field without any external work being done on the charge. This is because the electric field exerts a force on the charge in the same direction as the field, so no additional work is required to move the charge in that direction.

2) In a conductor under static conditions, all points must be at the same electric potential because electric charges in a conductor are free to move and redistribute themselves until they reach equilibrium. This means that the electric potential at any point in the conductor must be the same as the potential at any other point, otherwise there would be a non-zero electric field and the charges would continue to move until equilibrium is reached.