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Here is the full question from problem,

What are the magnitude and direction of the electric field that will balance the weight of the following?

An electron

A proton

For an electron/proton we use the equation $qE = mg$. Therefore the answer for magnitude would just to multiply the mass of an electron/proton by 9.8. But how come the direction for electron is upward, and proton is downward?

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Your question ask for the electric field, that in your equation is E. Also, the electric force must be the opposite of gravity so that both will cancel out, you are missing the minus sign:

$$ E = - { mg \over q } $$

Being $q = -1$ for the electron and $q = +1$ for the proton.

You can consider that $g$ is a vector pointing downwards, so $E$ for the electron will point downwards and for the proton it will point upwards.

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It should help you to consider the direction of the electric field generated by charges and what forces would act on a proton or electron positioned there.

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