Electric Field for Charge Distributions

[Jkalirai]

Homework Statement

a) Find the net force on charge 1.
b) What is the net electric field acting on charge 1?

Relevant Equations

F[SUB]E[/SUB] = k * q[SUB]1[/SUB] * q[SUB]2[/SUB] / r[SUP]2[/SUP]
ε = k * q / r^2

We are given: q₁ = +2.0 x 10^-5 C, q₂ = q₃ = -3.0 x 10^-5 C, r₃₁ = r₂₁ = 2 m

a) We start by finding the electric force between q₃ to q₁ and q₂ to q₁

F_E31 = k * q₁ * q₃ / r₃₁²

F_E31 = (9.0 x 10⁹ Nm²/C²) * (+2.0 x 10^-5 C) * (3.0 x 10^-5 C) / (2 m)²

F_E31 = 1.35 N

F_E21 = k * q₁ * q₂ / r₂₁²

Since q₂ = q₃ and r₃₁ = r₂₁

F_E21 = 1.35 N

Since the force of gravity is assumed to be negligible, we know that F_E21 = F_NETx and F_E31 = F_NETy

We can calculate F_NET from our components,

F_NET = √ [(1.35)² + (1.35)²]

F_NET = 1.9092 N

The angle of our net force can be calculated as well,

tanΘ = (1.35 N / 1.35N)

Θ = tan-1 (1.35N / 1.35 N)

Θ = 45^o

Therefore, the net force on charge 1 is equal to 1.91 N [N 45^o E].

b) To find ε on charge 1 we solve for the components of ε.

We know that q₂ = q₃ and r₂ = r₃

Therefore, ε₂ = ε₃

ε₂ = ε₃ = k * q / r²

ε = (9.0 x 10⁹ Nm²/C²) * (3.0 x 10^-5 C) / (2 m)²

ε = 6.75 x 10⁴ N/C

ε_NET = √ [(6.75 x 10⁴)² + (6.75 x 10⁴)²]

ε_NET = 95459.4155 N/C

Our angle will be,

Θ = tan-1 (6.75 x 104 N/C / 6.75 x 104 N/C)

Θ = 45^o

Therefore, our net electric field acting on charge 1 is 9.55 x 10⁴ N/C [N 45^o E].

I think my answer for part a) seems correct but for part b), I wanted to make sure it was right. It does seems to make sense when I think about it in my head, obviously the electric fields that are having an effect on charge A would be from charge B and C and their components would give me the net electric field. I've seen various different answers for part b) so I thought maybe I might be missing something. Anyways, I appreciate any input and thanks for giving this a read.

 

[haruspex]

You twice wrote ε = k * q / r, but correctly used ε = k * q / r².
You could have made it a bit easier by doing b first then multiplying by q₁.
You quote too many significant figures in the answers, given the precisions of the original data.
Other than that, looks fine.