Understanding Fundamentals of Electronics: Solving an Electric Charge Problem

• vasya
In summary: R##. Again, this is an approximation and may not be exact.The capacitance of a 1 cm3 sphere with a radius of 6.2 mm is about 4300 electrons.
vasya
Homework Statement
How many electrons will flow into the cube, connected to the 1.5v battery negative terminal, with positive being grounded
Relevant Equations
i dont know
It's not a homework. I came up with this problem myself. Trying to understand fundamentals of electronics. Do you know how to solve it? Is voltage somehow related to electron energy levels? What knowledge should I gain to be able to solve problems like that? Thank you!

If we ground the cathode (+) of a battery with, for example, 1.5v, and connect the anode (-) to an iron cube of 1 cm³

(26 protons in the nucleus,
density - 7.874 g/cm³
Atomic mass - 55.845 (g / mole)
chemical count - 0.1409 mole
atoms - 0.848 *10^22
protons - 22.06 *10^22 and the same number of electrons with zero charge)

How many electrons will flow into the cube, or what will be the charge in it?

ps: the electrostatic field of the Earth does not change, so it's not a capacitor, right?

By the way, if we will apply very high voltage to the cube, electrons will start to jump out of crystal lattice and fly away right?

Delta2
Hello @vasya,
Good questions, not so easy to answer at an appropriate level (which level that is in your case, isn't really known to us).

There is a relationship between charge and voltage$$Q = CV$$ with Q the charge, V the voltage and C the so-called capacitance. For the shape of the cube it's rather difficult, but for a sphere the capacitance can be shown to be ##C = 4\pi\varepsilon_0 R##, so that we get $$Q=4\pi\varepsilon_0 R \, V\ .$$A 1 cm3 sphere has a radius of 6.2 mm, so with 1 V we get a charge of 6.9 1013 Coulomb, which is about 4300 electrons.

yes, 6.9 times ten to the minus 13 Coulomb, of course. Sorry.
at first I had the 'Coulomb' inside the exponent and concentrated on fixing that...##\ ##

Last edited:
vasya, Delta2 and Lord Jestocost
vasya said:
Homework Statement:: How many electrons will flow into the cube, connected to the 1.5v battery negative terminal, with positive being grounded
Relevant Equations:: i don't know

How many electrons will flow into the cube, or what will be the charge in it?

ps: the electrostatic field of the Earth does not change, so it's not a capacitor, right?

By the way, if we will apply very high voltage to the cube, electrons will start to jump out of crystal lattice and fly away right?
This will have capacitance. Roughly it will be given by ##C= {4\pi{\epsilon}_0}\frac a 2 ## where a is side of cube. Then Q=VC

Given enough voltage (the work function) the electrons will be ejected from the metal. Usually they will bounce back but If this happens at a high enough rate and energy to cause ionization of the air a spark cascade will develop.

Last edited:
Delta2 and vasya
thank you all!

Delta2
Interesting problem you came up with, considering that you now beginning your studies to electricity/electromagnetism.
In my opinion both of the above answers are very good, just to ask @hutchphd , the formula for the cube must have a typo, it must be ##C=4\pi\epsilon_0\frac{a}{2}## and to emphasize that it is an approximation and not exact as in the case of a sphere.

Also to add that for your problem we must consider some assumptions:
1. That the grounded electrode has exactly 0V potential
2. The battery is ideal, and can maintain always 1.5V potential difference between the electrodes
3. The electrodes behave as ideal conductors.

hutchphd
BvU said:
A 1 cm3 sphere has a radius of 6.2 mm, so with 1 V we get a charge of 6.9 1013 Coulomb, which is about 4300 electrons.
It must be ##6.9\times 10^{-13}## right? (negative exponent I mean)

BvU and kuruman
Delta2 said:
That the grounded electrode has exactly 0V potential
I don't understand this requirement .
Thanks for the correction to my original post...I saw how badly I screwed it up immediately and think I corrected it before yours dropped. (Thought I had gotten away un-noticed.l...!)

Delta2
hutchphd said:
I don't understand this requirement .
Yes well i would better say that "The potential of each electrode is not affected by the charge of the other electrode".

hutchphd
Here is a paper on the numerical capacitance of a unit cube.

https://www.researchgate.net/publication/239582798_UNIT_CUBE_CAPACITANCE_CALCULATION_BY_MEANS_OF_FINITE_ELEMENT_ANALYSIS

hutchphd and Delta2
hutchphd said:
.I saw how badly I screwed it up immediately and think I corrected it before yours dropped. (Thought I had gotten away un-noticed.l...!)
The number of electrons too needs a correction.

Also, it would be interesting to do a capacitance measurement of a 1 cm cube vs. a similar sphere at some DC voltage. Since it would not by a typical 2 pole capacitor, any suggestions as how to do it? My initial guess would be to hook the negative terminal of a battery to the electrically isolated cube or sphere and the other terminal to ground. Would the capacitance be measured en between the cube or sphere and ground? Fluke digital multimeters have a capacitance setting and I was thinking of using that.

Last edited:
Correcting an earlier error I made, the average distance from the center to an edge of a unit cube is actually 0.640395!

This suggests ##C≈4 \pi \epsilon_0 (0.6404) a## where ##a## is the cube length.

The paper (no full access but the results are in the abstract) referenced below computes capacitance for a cube as; $$C=4 \pi \epsilon_0 (0.6606±0.0001) a$$
https://www.sciencedirect.com/science/article/abs/pii/S0304388604001044#:~:text=Our final result for the,therefore the best available value.

Another paper (check out the neat 3D plot of surface charge distribution!) with similar results;

https://www.cs.fsu.edu/~mascagni/papers/RIJP2003_6.pdf

Last edited:
Delta2

1. What is an electric charge?

An electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. It can be either positive or negative, and is measured in units of coulombs (C).

2. How do you calculate electric charge?

Electric charge is calculated by multiplying the number of charges (usually measured in electrons) by the elementary charge, which is approximately equal to 1.602 x 10^-19 coulombs. For example, if an object has 5 x 10^18 excess electrons, its electric charge would be -5 x 10^-1 coulombs.

3. What is the difference between electric charge and electric current?

Electric charge is a property of matter, while electric current is the flow of electric charge. Electric current is measured in units of amperes (A) and is the rate at which electric charge flows past a given point in a circuit.

4. How do you solve an electric charge problem?

To solve an electric charge problem, you must first identify the given information and what you are trying to find. Then, use the appropriate equations (such as the one for calculating electric charge) and substitute in the known values. Finally, solve for the unknown variable using algebraic manipulation.

5. What are some real-world applications of understanding electric charge?

Understanding electric charge is essential in many fields, including electronics, engineering, and physics. It is used in the design and operation of electrical circuits, batteries, and electronic devices. It is also crucial in understanding the behavior of lightning and other natural phenomena involving electricity.

• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Biology and Chemistry Homework Help
Replies
17
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
1K