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Pada titik sudut suatu segituga sama sisi ABC masing - masing terdapat muatan − 13 μ C , 6 μ C , dan 2 μ C . Panjang sisi segitiga itu 10 cm. Hitunglah usaha oran untuk memindahkan muatan − 2 μ C dari titik E (tengah - tengah AB ) ke F (tengah - tengah BC )!

Pada titik sudut suatu segituga sama sisi ABC  masing - masing terdapat muatan , dan . Panjang sisi segitiga itu 10 cm. Hitunglah usaha oran untuk memindahkan muatan  dari titik E (tengah - tengah AB ) ke F (tengah - tengah BC )!

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R. Haq

Master Teacher

Jawaban terverifikasi

Jawaban

usaha untuk memindahkan muatan tersebut dari E ke F sebesar -2,28 J.

usaha untuk memindahkan muatan tersebut dari E ke F sebesar -2,28 J.

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Pembahasan

Segitiga ABC dapat digambarkan sebagai berikut Hitung panjang CE dan AF Hitung potensial di titik E Hitung potensial di titik F Hitung usahanya Dengan demikian usaha untuk memindahkan muatan tersebut dari E ke F sebesar -2,28 J.

q subscript A equals negative 13 space μC equals negative 13 cross times 10 to the power of negative 6 end exponent space straight C q subscript B equals 6 space μC equals 6 cross times 10 to the power of negative 6 end exponent space straight C q subscript C equals 2 space μC equals 2 cross times 10 to the power of negative 6 end exponent space straight C s equals 10 space cm equals 0 comma 1 space cm q equals negative 2 space μC equals negative 2 cross times 10 to the power of negative 6 end exponent space straight C W subscript E F end subscript equals ?

Segitiga ABC dapat digambarkan sebagai berikut

 

Hitung panjang CE dan AF

table attributes columnalign right center left columnspacing 0px end attributes row cell C E end cell equals cell square root of A C squared minus A E squared end root end cell row blank equals cell square root of 10 squared minus 5 squared end root end cell row blank equals cell 5 square root of 3 space cm equals 5 square root of 3 cross times 10 to the power of negative 2 end exponent space cm end cell row blank blank blank row cell A F end cell equals cell C E equals 5 square root of 3 cross times 10 to the power of negative 2 end exponent space cm end cell end table

Hitung potensial di titik E

table attributes columnalign right center left columnspacing 0px end attributes row cell V subscript E end cell equals cell V subscript E A end subscript plus V subscript E B end subscript plus V subscript E C end subscript end cell row blank equals cell k q subscript A over r subscript A E end subscript plus k q subscript B over r subscript B E end subscript plus k q subscript C over r subscript C E end subscript end cell row blank equals cell k open parentheses q subscript A over r subscript A E end subscript plus q subscript B over r subscript B E end subscript plus q subscript C over r subscript C E end subscript close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses fraction numerator negative 13 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 6 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 2 cross times 10 to the power of negative 6 end exponent over denominator 5 square root of 3 cross times 10 to the power of negative 2 end exponent end fraction close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses fraction numerator negative 7 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 2 cross times 10 to the power of negative 6 end exponent over denominator 5 square root of 3 cross times 10 to the power of negative 2 end exponent end fraction close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses negative 1 comma 17 cross times 10 to the power of negative 4 end exponent close parentheses end cell row blank equals cell bold minus bold 1 bold comma bold 05 bold cross times bold 10 to the power of bold 6 bold space bold V end cell end table

Hitung potensial di titik F

table attributes columnalign right center left columnspacing 0px end attributes row cell straight V subscript straight F end cell equals cell straight V subscript FA plus straight V subscript FB plus straight V subscript FC end cell row blank equals cell straight k straight q subscript straight A over straight r subscript AF plus straight k straight q subscript straight B over straight r subscript BF plus straight k straight q subscript straight C over straight r subscript CF end cell row blank equals cell straight k open parentheses straight q subscript straight A over straight r subscript AF plus straight q subscript straight B over straight r subscript BF plus straight q subscript straight C over straight r subscript CF close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses fraction numerator negative 13 cross times 10 to the power of negative 6 end exponent over denominator 5 square root of 3 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 6 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 2 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses fraction numerator negative 13 cross times 10 to the power of negative 6 end exponent over denominator 5 square root of 3 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator 8 cross times 10 to the power of negative 6 end exponent over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses 9 comma 89 cross times 10 to the power of negative 6 end exponent close parentheses end cell row blank equals cell bold 8 bold comma bold 9 bold cross times bold 10 to the power of bold 4 bold space bold V end cell end table

Hitung usahanya

table attributes columnalign right center left columnspacing 0px end attributes row cell W subscript E F end subscript end cell equals cell E p subscript F minus E p subscript E end cell row blank equals cell q V subscript F minus q V subscript E end cell row blank equals cell q open parentheses V subscript F minus V subscript E close parentheses end cell row blank equals cell negative 2 cross times 10 to the power of negative 6 end exponent open parentheses 8 comma 9 cross times 10 to the power of 4 minus open parentheses negative 1 comma 05 cross times 10 to the power of 6 close parentheses close parentheses end cell row blank equals cell negative 2 cross times 10 to the power of negative 6 end exponent cross times 1 comma 14 cross times 10 to the power of 6 end cell row blank equals cell bold minus bold 2 bold comma bold 28 bold space bold J end cell end table

Dengan demikian usaha untuk memindahkan muatan tersebut dari E ke F sebesar -2,28 J.

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