Electric Force Calc: 4µC, -3µC, 4µC at 10cm, 4cm,-2cm

[redhot209]

Note: ^i means carrot on top of variable

Homework Statement

A particle with charge 4 µC is located on the x-axis at the point 10 cm, and a second particle with charge -3 µC is placed on the x-axis at 4 cm. What is the magnitude of the total electrostatic force on a third particle with a charge 4 µC placed on the x-axis at -2 cm? Answer in units of N.

The Attempt at a Solution

1) I converted all my variables to µC = C , and cm = m
q1 = 4 µC = 4e-6
q2 = -3 µC = -3e-6
q3 = 4 µC = 4e-6
x1 = 10 cm = 0.1 m
x2 = 4 cm = 0.04 m
x3 = -2 cm = -0.02 m

2 By using Coulom's law in vector form:
F₁₃= ke(q1q3/r²)^r₁₃
where ^r₁₃ is a unit vector directed from q1 to q3; i.e., ->r13 = ->r3 - ->r1

x13 = x3 - x1
(-0.02m)-(0.1m) = -0.12m
x23 = x3 - x2
(-0.02m)-(0.04) = -0.06 m

^x₁₃ = x₃-x₁/ √(x₃-x₁)^2 = -1 or -^i
^x₂₃ = x₃-x₂/ √(x₃-x₂)^2 = 1 or +^i

Since the forces are collinear, the force on the third particle is the algrebracis sum of the forces between the first and third and the second and third particles.

->F = ->F₁₃ + ->F₂₃
= k_e [q₁/ r²₁₃ X ^r₁₃ + q₂ / r²₂₃ x^r₁₃ ] q₃

After putting in the variables, I got 33.9444444445 N as my answer, but was wrong. What did i do wrong?

 

[rl.bhat]

First of all find the force between 4micro C at -2 cm and 4 micro C at 10 cm. It is repulsive force. Next find the force between 4micro C at -2 cm and -3 micro C at 4 cm. It is attractive force. Now find the net electrostatic force on the third charge.

 

[thomate1]

It seems like you have correctly applied Coulomb's law and calculated the forces between each pair of particles. However, when adding the forces together, you need to consider the direction of each force. The force between q1 and q3 is directed towards the left, while the force between q2 and q3 is directed towards the right. Therefore, when adding these two forces, they should be subtracted instead of added. This will give you a negative value for the total force, indicating that it is directed towards the left. Also, make sure to use the correct value for the Coulomb constant, which is 8.99 x 10^9 Nm^2/C^2. After making these corrections, you should get a magnitude of 27.83333333 N for the total electrostatic force on the third particle.