Pertanyaan

Pada keempat sudut persegi (sisi = 30 cm) diletakkan empat buah muatan yang sama ( 5 μ C ) . Tentukan kuat medan listrik di pusat persegi jikatanda keempat muatan itu adalah positif-positif-negatif-negatif dan jika kita mengitari persegi itu.

Pada keempat sudut persegi (sisi = 30 cm) diletakkan empat buah muatan yang sama $(5 μ C)$ . Tentukan kuat medan listrik di pusat persegi jika tanda keempat muatan itu adalah positif-positif-negatif-negatif dan jika kita mengitari persegi itu.

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Pembahasan

Jumlah medan listrik di pusat adalah: Jadi, resultan medan listrik di titik pusat sebesar ke arah bawah.

Jumlah medan listrik di pusat adalah:

E with rightwards harpoon with barb upwards on top open parentheses r with rightwards harpoon with barb upwards on top close parentheses equals sum from i equals 1 to N of E with rightwards harpoon with barb upwards on top open parentheses r with rightwards harpoon with barb upwards on top close parentheses

$E with rightwards harpoon with barb upwards on top open parentheses r with rightwards harpoon with barb upwards on top close parentheses equals E with rightwards harpoon with barb upwards on top open parentheses x comma y close parentheses E with rightwards harpoon with barb upwards on top open parentheses A close parentheses equals k fraction numerator q over denominator open parentheses begin display style s squared over 4 end style plus begin display style s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses i minus j close parentheses E with rightwards harpoon with barb upwards on top open parentheses B close parentheses equals k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative i minus j close parentheses E with rightwards harpoon with barb upwards on top open parentheses C close parentheses equals k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses i minus j close parentheses E with rightwards harpoon with barb upwards on top open parentheses D close parentheses equals k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative i minus j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals E with rightwards harpoon with barb upwards on top open parentheses A close parentheses plus E with rightwards harpoon with barb upwards on top open parentheses B close parentheses plus E with rightwards harpoon with barb upwards on top open parentheses C close parentheses plus E with rightwards harpoon with barb upwards on top open parentheses D close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses i minus j close parentheses plus 2 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative i minus j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative j close parentheses plus 2 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 4 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction 1 half square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 k fraction numerator q over denominator open parentheses begin display style s squared over 4 plus s squared over 4 end style close parentheses end fraction square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 k fraction numerator q over denominator open parentheses begin display style fraction numerator 0 comma 3 squared over denominator 4 end fraction plus fraction numerator 0 comma 3 squared over denominator 4 end fraction end style close parentheses end fraction square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 open parentheses 9 cross times 10 to the power of 9 close parentheses fraction numerator 5 cross times 10 to the power of negative 6 end exponent over denominator open parentheses begin display style 0 comma 045 end style close parentheses end fraction square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 open parentheses 9 cross times 10 to the power of 9 close parentheses fraction numerator 5 cross times 10 to the power of negative 6 end exponent over denominator open parentheses begin display style 0 comma 045 end style close parentheses end fraction square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 open parentheses 9 cross times 10 to the power of 9 close parentheses fraction numerator 5 cross times 10 to the power of negative 6 end exponent over denominator open parentheses begin display style 0 comma 045 end style close parentheses end fraction square root of 2 open parentheses negative j close parentheses E with rightwards harpoon with barb upwards on top open parentheses 0 comma 0 close parentheses equals 2 square root of 2 cross times 10 to the power of 6 open parentheses negative j close parentheses space bevelled straight N over straight C$

Jadi, resultan medan listrik di titik pusat sebesar ke arah bawah.

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