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

Written through Willy McAllister.

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

You don’t feel electric force in day-to-day life because practically every an adverse charge (electron) in the world is nestled increase close to a positive charge (the cell nucleus of one atom). The equalizes (neutralizes) the electrical force. It is why we space not mindful of it many of the time.

Thought experiment: compare the pressure of heaviness to the electric force between two apples.

## Gravitational force between two apples

A tool sized apple has a volume of around $100$ cubic centimeters and weighs roughly $100\,\textgrams$ (about $1/4$ pound). If you host an to apologize in your hand the downward force you feel is around $1$ newton. It is the force of attraction between the apple and the Earth. The is no too tough to lift an apple turn off the table. You are easily strong enough to overcome the gravitational attraction between the apple and also our planet.

What about the gravitational attraction between an apple and also another apple? It’s virtually nothing. You deserve to compute the tiny force using the regulation of Gravity,

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

Set $m_1$ and $m_2$ come $100\,\textgrams$. Ar the to 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 apologize is really close come $0$ force.

## Electric force in between two apples

Now for the electrical force. The electrical force in between apples is $0$. That’s due to the fact that there space equal number of $+$ and $-$ dues in both apples and also everything is electrically neutral.

That’s no really a same comparison v gravity, due to the fact that the plus and also minus charges are all intermingled. Let’s fee one apple up to $+1$ coulomb and the other to $-1$ coulomb. $1$ coulomb is the amount of fee that moves past a allude in a cable in $1\,\textsecond$ once the existing is $1\,\textampere$. That’s a reasonable everyday current.

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

What is the pressure of attraction? the is gigantic! us compute the electrical force through Coulomb’s Law. The force between two $1$ coulomb charges inserted $1$ 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 pressure you would feel if **ten** fully loaded oil supertankers to be sitting on your head.

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

## Background

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

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

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

There are practically exactly $10,000\,\textcoulombs$ of negative charge in $1\,\textmole$ of electrons.

If you eliminate $1$ electron native $1$ the end of every $55,000$ molecule in an apple, it adds up to $1\,\textcoulomb$ that electrons.

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