Question

The charges and coordinates of two charged particles held fixed in an xy plane are q₁ = 2.55 μC, x₁ = 5.88 cm, y₁ = 0.699 cm and q₂ = -4.34 μC, x₂ = -2.79 cm, y₂ = 1.92 cm. Find the (a) magnitude and (b) direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge q₃ = 6.77 μC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

Answer 1

The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 2.55 μC, x1 = 5.88 cm, y1 = 0.699 cm and q2 = -4.34 μC, x2 = -2.79 cm, y2 = 1.92 cm

A).

The distance between two points on the xy plane is given by

On substitution of given values

r=8.756cm or 0.08756m

The electrostatic force magnitude on particle 2 due to particle 1 [coulomb's law]

On substitution of given values

B).

Direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle.

From the slope of the line between the two particles

°

C).

Let a third particle of charge q3 = 6.77 μC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero.

so

On simplification

On substitution of given values

​​​​​from B ° direction

Let the third particle position be X3, Y3

We have

Answers

A.

B.

C. and