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Dua buah muatan listrik 1 μC dan -3 μC terletak pada jarak 10 cm. Berapakah kuat medan listrik di titik pertengahan ?

Pertanyaan

Dua buah muatan listrik 1 μC dan -3 μC terletak pada jarak 10 cm. Berapakah kuat medan listrik di titik pertengahan ? 

Pembahasan Soal:

Diketahui :

q subscript 1 equals 1 space μC equals 10 to the power of negative 6 end exponent space straight C q subscript 2 equals negative 3 space μC equals negative 3 times 10 to the power of negative 6 end exponent space straight C r equals 10 space cm equals 10 to the power of negative 1 end exponent space straight m r subscript 1 equals 5 space cm equals 5 times 10 to the power of negative 2 end exponent space straight m r subscript 2 equals 5 space cm equals 5 times 10 to the power of negative 2 end exponent space straight m k equals 9 times 10 to the power of 9 space Nm squared straight C squared

Ditanya :

E equals ? di titik pertengahan

Jawab :

Kuat medan listrik di titik yang berada di tengah muatan q1 dan q2 :

E equals E subscript 1 plus E subscript 2 E equals fraction numerator k q subscript 1 over denominator r subscript 1 squared end fraction plus fraction numerator k q subscript 2 over denominator r subscript 2 squared end fraction E equals k open parentheses q subscript 1 over r subscript 1 squared plus q subscript 2 over r subscript 2 squared close parentheses E equals 9 times 10 to the power of 9 open parentheses 10 to the power of negative 6 end exponent over open parentheses 5 times 10 to the power of negative 2 end exponent close parentheses squared plus fraction numerator 3 times 10 to the power of negative 6 end exponent over denominator open parentheses 5 times 10 to the power of negative 2 end exponent close parentheses squared end fraction close parentheses E equals 9 times 10 to the power of 9 open parentheses fraction numerator 10 to the power of negative 6 end exponent over denominator 25 times 10 to the power of negative 4 end exponent end fraction plus fraction numerator 3 times 10 to the power of negative 6 end exponent over denominator 25 times 10 to the power of negative 4 end exponent end fraction close parentheses E equals 9 times 10 to the power of 9 open parentheses 4 times 10 to the power of negative 4 end exponent plus 12 times 10 to the power of negative 4 end exponent close parentheses E equals 9 times 10 to the power of 9 open parentheses 16 times 10 to the power of negative 4 end exponent close parentheses E equals 144 times 10 to the power of 5 E equals 1 comma 44 times 10 to the power of 7 space straight N divided by straight C

Jadi kuat medan listrik di titik yang berada tengah-tengah kedua muatan adalah 1 comma 44 times 10 to the power of 7 N/C .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Syarif

Mahasiswa/Alumni Universitas Negeri Padang

Terakhir diupdate 08 September 2021

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Pembahasan Soal:

Kuat space medan space listrik space muatan space 1 space yang space dirasakan space oleh space titik space straight P space adalah colon  straight E subscript 1 equals straight k fraction numerator straight q subscript 1 over denominator straight R subscript 1 superscript 2 end fraction equals left parenthesis 9 space straight x space 10 to the power of 9 right parenthesis space fraction numerator left parenthesis 40 space straight x space 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 40 space straight x space 10 to the power of negative 2 end exponent right parenthesis squared end fraction equals 2 comma 25 space straight x space 10 to the power of 6 space straight N divided by straight C

Kuat space medan space listrik space muatan space 2 space yang space dirasakan space oleh space titik space straight C space adalah colon  straight E subscript 2 equals straight k fraction numerator straight q subscript 2 over denominator straight R subscript 2 superscript 2 end fraction equals left parenthesis 9 space straight x space 10 to the power of 9 right parenthesis space fraction numerator left parenthesis 5 space straight x space 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 10 space straight x space 10 to the power of negative 2 end exponent right parenthesis squared end fraction equals 4 comma 5 space straight x space 10 to the power of 6 space straight N divided by straight C  Maka comma space kuat space medan space listrik space total space yang space dirasakan space oleh space titik space straight C space adalah

straight E subscript straight c equals straight E subscript 2 minus straight E subscript 1  straight E subscript straight c space equals left parenthesis 4 comma 5 space minus space 2 comma 25 right parenthesis space straight x space 10 to the power of 6  straight E subscript straight c space equals space 2 comma 25 space straight x space 10 to the power of 6 space end exponent straight N divided by straight C

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Dua buah muatan listrik terpisah seperti gambar Titik C di antara kedua muatan berjarak 10 cm dari A. Jika   ,  maka besar kuat medan listrik di titik X karena pengaruh kedua muatan adalah ...

Pembahasan Soal:

straight R subscript straight A equals space 10 cm equals space 1 cross times 10 to the power of negative 1 end exponent straight m  straight R subscript straight B equals space 20 space cm space equals space 2 cross times space 10 to the power of negative 1 end exponent straight m  straight q subscript straight A equals space 2 μC equals space 2 space cross times space 10 to the power of negative 6 end exponent straight C  straight q subscript straight B equals negative 4 μC space equals space minus 4 space cross times 10 to the power of negative 6 end exponent space straight C

Kuat space medan space listrik space straight A space dirasakan space oleh space straight C space adalah space colon  straight E subscript straight A equals straight k straight q subscript straight a over straight R squared subscript straight A equals left parenthesis 9 cross times 10 to the power of 9 right parenthesis fraction numerator left parenthesis 2 cross times 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 1 cross times 10 to the power of negative 1 end exponent right parenthesis squared end fraction equals space 18 cross times 10 to the power of 5 bevelled straight N over straight C  Kuat space medan space listrik space straight B space yang space dirasakan space oelh space straight C space adalah space colon    straight E subscript straight B equals straight k straight q subscript straight B over straight R squared subscript straight B equals left parenthesis 9 cross times 10 to the power of 9 right parenthesis fraction numerator left parenthesis 4 cross times 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 2 cross times 10 to the power of negative 1 end exponent right parenthesis squared end fraction equals space 9 cross times 10 to the power of 5 bevelled straight N over straight C  Maka space kuat space medan space listrik space total space yang space dirasakan space oleh space straight C space adalah colon  straight E subscript straight C equals straight E subscript straight B plus straight E subscript straight A  straight E subscript straight C equals left parenthesis 18 plus 9 right parenthesis cross times 10 to the power of 5  straight E subscript straight C equals 27 space cross times 10 to the power of 5 bevelled straight N over straight C

 

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Dua buah partikel A dan B masing-masing bermuatan listrik +20 µC dan +45 µC terpisah dengan jarak 15 cm. Jika C adalah titik yang terletak di antara A dan B sedemikian sehingga medan di C sama dengan ...

Pembahasan Soal:

Medan listrik di C sama dengan 0, maka

E subscript A equals E subscript B k q subscript A over r subscript A C end subscript squared equals k q subscript B over r subscript B C end subscript squared q subscript A over r subscript A C end subscript squared equals q subscript B over r subscript B C end subscript squared fraction numerator 20.10 to the power of negative 6 end exponent over denominator x squared end fraction equals fraction numerator 45.10 to the power of negative 6 end exponent over denominator left parenthesis 15 minus x right parenthesis squared end fraction 4 over x squared equals 9 over left parenthesis 15 minus x right parenthesis squared 2 over x equals fraction numerator 3 over denominator 15 minus x end fraction 30 minus 2 x equals 3 x 5 x equals 30 x equals 6 space cm

Dengan demikian, jawaban yang tepat adalah D

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Perhatikan gambar berikut ! Muatan q3​ diletakkan pada jarak 5 cm dari q2​, maka kuat medan listrik pada muatan  adalah .... (1μC=10−6C)

Pembahasan Soal:

straight R subscript 1 equals 5 space cm equals 5 cross times 10 to the power of negative 2 end exponent space straight m  straight R subscript 2 equals 10 space cm minus 5 space cm equals 5 space cm equals 5 space straight x space 10 to the power of negative 2 end exponent space straight m

Muatan space straight q subscript 3 space diletakkan space pada space jarak space 5 space cm space dari space straight q subscript 2 space diantara space straight q subscript 1 dan space straight q subscript 2  maka space kuat space medan space listrik space pada space muatan space straight q subscript 3 space yaitu

straight E space equals space straight E subscript 1 minus straight E subscript 2  straight E space equals space straight k open parentheses fraction numerator straight q 1 over denominator straight R subscript 1 superscript 2 end fraction minus fraction numerator straight q 2 over denominator straight R subscript 2 superscript 2 end fraction close parentheses  straight E space equals space 9 space straight x space 10 to the power of 9 open parentheses fraction numerator 5 space straight x space 10 to the power of negative 6 end exponent over denominator left parenthesis space 5 space straight x space 10 squared right parenthesis squared end fraction minus fraction numerator negative 5 space straight x space 10 to the power of negative 6 end exponent over denominator left parenthesis space 5 space straight x space 10 to the power of negative 2 end exponent right parenthesis squared end fraction close parentheses  straight E space equals space 9 space straight x space 10 to the power of 9 left parenthesis 0 comma 4 space straight x space 10 to the power of negative 2 end exponent right parenthesis  straight E space equals space 3 comma 6 space straight x space 10 to the power of 7 space straight N divided by straight C

1

Roboguru

Perhatikan gambar berikut! Muatan q3​ diletakkan pada jarak 5 cm dari q2​, maka kuat medan listrik pada muatan  adalah .... (1μC=10−6C)

Pembahasan Soal:

straight R subscript straight A equals 5 space cm equals 5 cross times 10 to the power of negative 2 end exponent space straight m  straight R subscript straight B equals 5 space cm equals 5 cross times 10 to the power of negative 2 end exponent space straight m

Kuat medan listrik A yang dirasakan oleh q3 adalah :

straight E subscript straight A equals straight k fraction numerator straight q subscript straight A over denominator straight R subscript straight A superscript 2 end fraction equals left parenthesis 9 cross times 10 to the power of 9 right parenthesis left parenthesis fraction numerator left parenthesis 5 cross times 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 5 cross times 10 to the power of negative 2 end exponent right parenthesis squared end fraction equals 1 comma 8 cross times 10 to the power of 7 space straight N divided by straight C

Kuat medan listrik B yang dirasakan oleh q3 adalah :

straight E subscript straight B equals straight k fraction numerator straight q subscript straight B over denominator straight R subscript straight B superscript 2 end fraction equals left parenthesis 9 cross times 10 to the power of 9 right parenthesis fraction numerator left parenthesis 5 cross times 10 to the power of negative 6 end exponent right parenthesis over denominator left parenthesis 5 cross times 10 to the power of negative 2 end exponent right parenthesis squared end fraction equals 1 comma 8 cross times 10 to the power of 7 space straight N divided by straight C

Maka, kuat medan listrik total yang dirasakan oleh q3 adalah :

straight E subscript straight C equals straight E subscript straight B plus straight E subscript straight A  straight E subscript straight C equals left parenthesis 1 comma 8 plus 1 comma 8 right parenthesis cross times 10 to the power of 7  straight E subscript straight C equals 3 comma 6 cross times 10 to the power of 7 space straight N divided by straight C

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Roboguru

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