Question

part a
if a television set were laid on its back, would electrons be able to move upward against the force of gravity?
the electrons would be able to move upward against the force of gravity.
the electrons would not be able to move upward against the force of gravity.
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part b
what potential difference, acting over a distance of 4.4 cm, would be needed to balance the downward force of gravity so that an electron would remain stationary? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Analyze the force on electrons

When an electron is in an electric field \(E\), the electric force \(F_e = eE\), and the gravitational force \(F_g=mg\). For the electron to be stationary \(F_e = F_g\), so \(eE=mg\). Also, \(E=\frac{V}{d}\), then \(e\frac{V}{d}=mg\), and \(V = \frac{mgd}{e}\).

Step2: Substitute the known values

The mass of an electron \(m = 9.1\times10^{-31}\space kg\), the charge of an electron \(e=1.6\times 10^{-19}\space C\), \(g = 9.8\space m/s^{2}\), and \(d=4.4\times10^{-2}\space m\).
Substitute these values into the formula \(V=\frac{mgd}{e}\):

$$
LATEXBLOCK0
$$

$$
LATEXBLOCK1
$$

So \(V=245.245\times10^{-14}\space V\approx2.5\times 10^{-12}\space V\)

Answer:

For Part A: The electrons would be able to move upward against the force of gravity. Because the electric force on electrons in a television (cathode - ray tube) is much larger than the gravitational force. The electric force accelerates electrons, and the gravitational force is negligible in comparison.
For Part B: \(V = 2.5\times10^{-12}\space V\)