Question

Two point-like charges are placed at the corners of a square, a = 34.0 cm. Find the magnitude of the electric field at the bottom left corner. Let q1 = −1.40 µC, and q2 = −3.00 µC. q1 is top right corner and q2 is bottom right corner.

Answer 1

$a=34cm=0.34m$

$d=\sqrt{2}*a=0.481m$

$E=kq/r^{2}$

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$E_{2}=kq_{2}/a^{2}$

$E_{2}=9*10^{9}*3*10^{-6}C/(0.34m)^{2}$

${\color{Red} E_{2}=233564.01N/C}$

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$E_{1}=kq_{1}/d^{2}$

$E_{1}=9*10^{9}*1.4*10^{-6}C/(0.481m)^{2}$

${\color{Red} E_{1}=54460.35N/C}$

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$E_{x}=E_{2}+E_{1}cos45$

$E_{x}=233564.01N/C+54460.35N/C*cos45$

${\color{Red} E_{x}=272073.29N/C}$

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$E_{y}=E_{1}sin45$

$E_{y}=54460.35*sin45$

${\color{Red} E_{y}=38509.28N/C}$

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$E=\sqrt{E_{x}^{2}+E_{y}^{2}}$

$E=\sqrt{(272073.29)^{2}+(38509.28)^{2}}$

ANSWER:${\color{Red} E=274785.08N/C}$

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