Why does Sal to speak (at 4:40) the gravitational force is weak contrasted to the electrical force?

Written by Willy McAllister.

You are watching: The electrical force is much weaker than the force of gravity.

You nothing feel electric force in everyday life because virtually every negative charge (electron) in the cosmos is nestled increase close to a positive charge (the cell nucleus of one atom). That equalizes (neutralizes) the electric force. It is why we room not mindful of it many of the time.

Thought experiment: compare the pressure of gravity to the electrical force between two apples.

## Gravitational force between two apples

A medium sized apple has a volume of about $100$ cubic centimeters and weighs around $100\,\textgrams$ (about $1/4$ pound). If you organize an apologize in your hand the downward pressure you feeling is around $1$ newton. That’s the pressure of attraction between the apple and also the Earth. It is not too difficult to lift an apple off the table. You room easily strong enough to get over the gravitational attraction in between the apple and also our planet.

What around the gravitational attraction between an apple and another apple? It’s nearly nothing. You deserve to compute the tiny pressure using the legislation of Gravity,

$F = G \,\dfracm_1 \, m_2r^2\qquad$ wherein $G = 6.67 \times 10^-11\,\text N \, \text m^2/\textkg^2$

Set $m_1$ and $m_2$ to $100\,\textgrams$. Place the apologize $1\,\textmeter$ apart, $r = 1\,\textmeter$.

$F = 6.67 \times 10^-11 \times \dfrac0.1 \times 0.11^2$

$F = 6.67 \times 10^-13\,\text N$

The attraction in between two to apologize is yes, really close to $0$ force.

## Electric force between two apples

Now for the electric force. The electric force between apples is $0$. That’s since there space equal numbers of $+$ and also $-$ dues in both apples and also everything is electrically neutral.

That’s not really a fair comparison v gravity, since the plus and also minus charges are all intermingled. Let’s fee one apple up to $+1$ coulomb and also the various other to $-1$ coulomb. $1$ coulomb is the amount of fee that moves past a allude in a wire in $1\,\textsecond$ when the existing is $1\,\textampere$. It is a reasonable day-to-day current.

To charge an apple up to a coulomb you can (conceptually) remove $1$ electron because that every $55,000$ water molecules, leaving an apple through a $+1\,\text C$ charge. Take the electron and put that on the other apple to offer it a $-1\,\text C$ charge. (See the Background ar below.)

What is the force of attraction? that is gigantic! we compute the electrical force v Coulomb’s Law. The force in between two $1$ coulomb charges put $1$ meter apart is,

$|\vec F| = K \dfracq_0 \,q_1r^2$

$K = 9 \times 10^9\, \textnewton-meter^2/\textcoulomb^2$

$|\vec F| = 9 \times 10^9 \times \dfrac1 \times 11^2$

$|\vec F| = 9 \times 10^9 \,\textnewtons$ (attracting)

This is the force you would certainly feel if ten completely loaded oil supertankers were sitting on her head.

The electrical force is unimaginably better than the pressure of gravity.

## Background

The mole is defined by Avogadro’s Number, $6.022 \times 10^23$ particles.

$1\,\textmole$ of $\text H_2\text O$ weighs $18\,\textgrams$. $2\,\textgrams$ that hydrogen plus $16\,\textgrams$ of oxygen.

An apple is mostly water. $100\,\textgrams$ of water is $100\,\text g/(18\,\text g/\textmole) = 5.5\,\textmoles$ of mainly water molecules.

There are almost exactly $10,000\,\textcoulombs$ of an unfavorable charge in $1\,\textmole$ that electrons.

If you remove $1$ electron from $1$ the end of every $55,000$ molecules in an apple, that adds up to $1\,\textcoulomb$ the electrons.

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$1\,\textnewton$ is around $0.1\,\textkilogram$$1000 \,\textkilograms = 1\,\textmetric tonne$$1\,\texttonne \approx 10^4\,\textnewtons$$9\times 10^9\,\textnewtons$ is around $9\times 10^9/10^4 = 900,000\,\texttonnes$.A totally loaded LR2 supertanker weighs about $90,000\,\texttonnes$.