Why, in a conservative field, does the force equal the negative

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Anonymous
2017-08-31 12:11:31 Post No. 9139365
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Anonymous 2017-08-31 12:11:31 Post No. 9139365 [Report]

Why, in a conservative field, does the force equal the negative gradient of the potential?

[math]F=- \nabla V[/math]

I know this relationship is true, but WHY is it that way?

Anonymous 2017-08-31 12:18:52 Post No.9139382
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Anonymous 2017-08-31 12:18:52 Post No.9139382 [Report]

It's the fucking definition.

Anonymous 2017-08-31 01:12:32 Post No.9139452
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Anonymous 2017-08-31 01:12:32 Post No.9139452 [Report]

>>9139382
It is?

Anonymous 2017-08-31 07:24:37 Post No.9139930
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Anonymous 2017-08-31 07:24:37 Post No.9139930 [Report]

>>9139365
its just from how V and momentum is defined, you could redefine the fields in such a way that there is no minus, but then some other equations will get a negative in it.

Why, in a conservative field, does the force equal the negative

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