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I am studying electricity and until about now I never really gave much thought to the statement that equal number of proton and electron means neutral charge. Like if we simplify the question and consider two point charges, one is positive and another negative, exactly what is happening to the electric field produced by the individual positive and negative charges that when they attract each other, we say that there is no charge? Like does the respective electric field produced by them disappear? What exactly does neutral charge mean? Do neutral objects that have equal number of proton and electron no longer feel electric field?

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exactly what is happening to the electric field produced by the individuals positive and negative charge that when they attract each other, we say that there is no charge?

If the amount of positive and negative charge is equal, then the net charge is zero. That is not the same thing as saying there is no charge.

Like does the respective electric field produced by them disappear?

No. Those fields don't "disappear".

For example, if another negative charge were brought nearby it would experience an attractive force by the field of the positive point charge and a repulsive force by the field of the negative point charge.

What exactly does neutral charge mean?

Simply that the amount of positive and negative charge is equal.

Do neutral objects that have equal number of proton and electron no longer feel electric field?

I assume you are asking if the neutral object would "feel" an electric field produced by some other negatively (or positively) charged object. That would depend on how the positive and negative charges are distributed on the neutral object.

For example polar molecules, where the charge distribution is spherically asymmetrical (resulting in a dipole moment), such as water, will interact with an external electric field causing it to rotate, whereas non polar molecules where the charge distribution is spherically symmetrical, such as carbon dioxide, will not interact with electric fields.

Hope this helps.

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