Solucions Física en context 2: Q41

Q41

Calculeu la força elèctrica que actua entre dues càrregues iguals a 10 nC separades 5 cm de distància:

a) En el buit.

En el següent enllaç teniu les diferents permitivitats relatives:
http://cesire.cat.mialias.net/recursos/context/fisica/unitat%2010/222_la_fora_elctrica.html

La permitivitat relativa del buit és 1:

$F equals k times fraction numerator Q times Q over denominator r squared end fraction equals fraction numerator 1 over denominator 4 times straight pi times straight epsilon subscript straight o end fraction times fraction numerator Q times Q over denominator r squared end fraction$

$F equals 9 times 10 to the power of 9 times fraction numerator 10 times 10 to the power of negative 9 end exponent times 10 times 10 to the power of negative 9 end exponent over denominator 0 comma 05 squared end fraction$

$box enclose F equals 3 comma 6 times 10 to the power of negative 4 end exponent space N end enclose$

b) En l'aigua

La permitivitat relativa de l'aigua és 81:

$F equals k times fraction numerator Q times Q over denominator r squared end fraction equals fraction numerator 1 over denominator 4 times straight pi times straight epsilon end fraction times fraction numerator Q times Q over denominator r squared end fraction equals fraction numerator 1 over denominator 4 times straight pi times straight epsilon subscript straight o times straight epsilon subscript straight r end fraction times fraction numerator Q times Q over denominator r squared end fraction$

$F equals fraction numerator 9 times 10 to the power of 9 over denominator 81 end fraction times fraction numerator 10 times 10 to the power of negative 9 end exponent times 10 times 10 to the power of negative 9 end exponent over denominator 0 comma 05 squared end fraction$

$box enclose F equals 4 comma 44 times 10 to the power of negative 6 end exponent space N end enclose$

c) En l'aire

La permitivitat relativa de l'aire és 1,00059:

$F equals fraction numerator 9 times 10 to the power of 9 over denominator 1 comma 00059 end fraction times fraction numerator 10 times 10 to the power of negative 9 end exponent times 10 times 10 to the power of negative 9 end exponent over denominator 0 comma 05 squared end fraction$

$box enclose F equals 3 comma 597877 times 10 to the power of negative 4 end exponent space N end enclose$

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Q41