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A positive charge is fixed at point (−4,−3) and a negative charge − is fixed at point (−4,0). Determine the net electric force ⃗ net acting on a positive test charge + at the origin (0,0) in terms of the given quantities and physical constants, including the permittivity of free space 0. Express the force using unit vector notation. Enter precise fractions rather than entering their approximate numerical values.

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onyebuchinnaji

The net electric force acting on a positive test charge at the origin is determined as ¹/₉(kq₁q₂).

Net electric force on the charges

The net electric force on the charges is calculated as follows;

F = kq₁q₂/r²

where;

  • k is coulomb's constant
  • q₁ and q₂ are the charges
  • r is the distance between the charges

Distance between the charges

[tex]|r| = \sqrt{(x_2-x_1)^2+ (y_2-y_1)^2} \\\\|r| = \sqrt{(-4--4)^2+ (0--3)^2} \\\\|r| = \sqrt{(0)^2 + (3)^2} \\\\|r| = 3 \ units[/tex]

[tex]F_{net} = \frac{kq_1q_2}{3^2} \\\\F_{net} = \frac{1}{9} (kq_1q_2) , \ N[/tex]

Thus, the net electric force acting on a positive test charge at the origin is determined as ¹/₉(kq₁q₂).

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