Chapter 17, Problem 58GP

To determine

Weather the electron would be able to move upward against the force of the gravity and determine the potential difference that acts over the distance of 3.0 cm that would be needed to balance the downward force of the gravity so that the electron would remain stationary.

Answer to Problem 58GP

The electron will move upward and the electric potential will be of $1.7\times {10}^{-12}\text{V}$ also the electron force on the electron have the same magnitude as the weight of the electron.

Explanation of Solution

Given info:

Assume that the electric field is uniform.

Formula Used:

The required diagram is shown in Figure 1

  

Figure 1

The formula to determine the value of the potential difference is,

  $V=\frac{mgd}{e}$

Calculation:

Consider the electron is moving the electric field as the tube is laid on the back and it depends on the voltage applied, here the electron may or may not move against the force of the gravity.

In case the electrical potential is high then the electron overcome the force of the gravity and it move upward.

The electron force on the electron have the same magnitude as the weight of the electron.

The value of the voltage is calculated as,

  $\begin{array}{c}V=\frac{\left(9.11\times {10}^{-31}\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2\right)\left(3.0\times {10}^{-2}\text{m}\right)}{1.6\times {10}^{-19}\text{C}}\\ =1.7\times {10}^{-12}\text{V}\end{array}$

Conclusion:

Therefore, the electron will move upward and the electric potential will be of $1.7\times {10}^{-12}\text{V}$ also the electron force on the electron have the same magnitude as the weight of the electron.