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Bujur sangkar ABCD berisi 10 cm. Pada titik sudutnya terdapat muatan sebesar 9 μ C , 5 μ C , − 4 μ C , − 8 μ C , hitunglah potensial di titik E (tengah - tengah AB )!

Bujur sangkar ABCD berisi 10 cm. Pada titik sudutnya terdapat muatan sebesar , hitunglah potensial di titik E (tengah - tengah AB)!

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Jawaban terverifikasi

Jawaban

potensial di titik E sebesar

potensial di titik E sebesar bold 1 bold comma bold 56 bold cross times bold 10 to the power of bold 6 bold space bold V    

Pembahasan

Bujur sangkar ABCD dapat digambarkan seperti berikut Hitung panjang DE dan CE Titik E mengalami potensial akibat muatan pada A, B, C, dan D sehingga potensial dititik E dapat dihitung menggunakan persamaan Dengan demikian potensial di titik E sebesar

s equals 10 space cm q subscript A equals 9 space μC q subscript B equals 5 space μC q subscript C equals negative 4 space μC q subscript D equals negative 8 space μC V subscript E equals ?

Bujur sangkar ABCD dapat digambarkan seperti berikut

 

Hitung panjang DE dan CE

D E equals square root of A D squared plus A E squared end root D E equals square root of s squared plus open parentheses 1 half s close parentheses squared end root D E equals square root of 10 squared plus 5 squared end root D E equals 5 square root of 5 space cm equals 5 square root of 5 cross times 10 to the power of negative 2 end exponent space straight m  C D equals D E equals 5 square root of 5 cross times 10 to the power of negative 2 end exponent space straight m 

Titik E mengalami potensial akibat muatan pada A, B, C, dan D sehingga potensial dititik E dapat dihitung menggunakan persamaan

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 plus V subscript E D 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 plus k q subscript D over r subscript D E end subscript end cell row blank equals cell k open parentheses fraction numerator q subscript A over denominator begin display style 1 half end style s end fraction plus fraction numerator q subscript B over denominator begin display style 1 half end style s end fraction plus fraction numerator q subscript C over denominator C E end fraction plus fraction numerator q subscript D over denominator D E end fraction close parentheses end cell row blank equals cell 9 cross times 10 to the power of 9 open parentheses fraction numerator 9 cross times 10 to the power of negative 6 end exponent over denominator begin display style 1 half end style cross times 0 comma 1 end fraction plus fraction numerator 5 cross times 10 to the power of negative 6 end exponent over denominator begin display style 1 half end style cross times 0 comma 1 end fraction plus fraction numerator open parentheses negative 4 plus-or-minus 10 to the power of negative 6 end exponent close parentheses over denominator 5 square root of 5 cross times 10 to the power of negative 2 end exponent end fraction plus fraction numerator open parentheses negative 8 cross times 10 to the power of negative 6 end exponent close parentheses over denominator 5 square root of 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 14 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 minus fraction numerator 12 cross times 10 to the power of negative 6 end exponent over denominator 5 square root of 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 cross times 1 comma 73 cross times 10 to the power of negative 4 end exponent end cell row blank equals cell 1 comma 56 cross times 10 to the power of 6 space straight V end cell end table

Dengan demikian potensial di titik E sebesar bold 1 bold comma bold 56 bold cross times bold 10 to the power of bold 6 bold space bold V    

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