# Help With a Physics Question Involving Electrons and Gravitational Force

• Jodi
In summary, the conversation discusses the acceleration of an electron in a uniform electric field between two parallel charged plates. The speed at which the electron leaves the positive plate's hole is calculated to be 7.49E6 m/s. The question of whether the gravitational force can be ignored is raised, and it is concluded that the force of gravity is much weaker than the electric force on a micro-scale. The conversation also mentions using the masses and radii of the electron and plate to approximate the necessary mass to accelerate the electron with 1/100th of the electric field's acceleration, but it is noted that the Earth's gravity is about 14 orders of magnitude weaker than the electric field.
Jodi
Hi; Could someone please help me with this question: An electron (m= 9.11E-31 kg) is accelerated in the uniform field E (E= 1.45 x 10^4 N/C) b/w two parallel charged plates. The separation of the plates is 1.10cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate a)With what speed does it leave the hole? (I got the answer to this, which was 7.49E6 m/s. b) Show that the gravitational force can be ignored. I do not understand how to answer part b. Could somebody please help me. Thank you.

Just show that the force of gravitation is so small that it can be ignored. Do you know the mass of the plate? If so,just use the force equation for gravity to find the net acceleration.

if not, you can just do a magnitudal analysis, the electron has mass of ~10^-31, the radius is ~10^-2 and G is 10^-11, using the equation for gravitational force, approximate the mass that the plate would need to accelerate the electron to that final speed. The mass should be somewhere in the range of 10^30kg (heavier than the mass of the earth).

You can then say that to accelerate the electron with 1/100th of the E field acceleration you would need a mass 100 times smaller,~ (10^28kg) which is still a couple thousand times heavier than earth.

I hope you can draw from this that gravity is much weaker than the EM force when it comes to the micro-scale.

I think it's a bit simpler than that...

Haha, what is all this silliness about the mass of the plate or the radius of the electron? I think "gravitational force" simply means Earth's gravity, no?

We simply say, $$F_g = mg$$ and $$F_E = qE$$ .

Now, $$F_g \approx 10^{-29} N$$ and $$F_E \approx 10^{-15} N$$. (The charge of the electron is about $$1.6 \times 10^{-19}C$$).

Well, $$\frac{F_g}{F_E} \approx \frac{10^{-29}}{10^{-15}} = 10^{-14}$$.

This means the Earth's gravitational force is about 14 orders of magnitude weaker than the electric field of the plate, or one one hundredth trillionth. Negligible.

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That makes sense too, and is probably the method they are lookin for. They really should be more specific though, as mine is just as correct given the vagueness of the problem .

given the vagueness of the problem .

True... reminds me of what my professor says: grad students get to such advanced levels that when they come across a truly simple problem, they don't know how to deal with it because they've been doing the hard stuff for so long.

## 1. How do electrons interact with gravitational force?

Electrons are negatively charged particles that are affected by the gravitational force of larger objects, such as planets and stars. This force causes electrons to be pulled towards the center of the object, just like any other object with mass.

## 2. Can electrons defy the laws of gravity?

No, electrons cannot defy the laws of gravity. They are subject to the same gravitational force as any other object with mass. However, due to their small size and low mass, the effects of gravity on individual electrons are often negligible.

## 3. How does the gravitational force between electrons and protons affect atoms?

The gravitational force between electrons and protons is relatively weak compared to the electromagnetic force that holds atoms together. Therefore, the gravitational force does not have a significant impact on the overall structure of atoms.

## 4. Can the gravitational force between electrons and protons be measured?

Yes, the gravitational force between electrons and protons can be measured using sophisticated instruments and techniques. However, due to the small size and low mass of electrons, the force is often difficult to detect and measure accurately.

## 5. How does the gravitational force affect the behavior of electrons in orbit around the nucleus?

The gravitational force does not play a significant role in the behavior of electrons in orbit around the nucleus. Rather, it is the electromagnetic force that keeps electrons in their respective energy levels and determines their movement around the nucleus.

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