Calculating Two Unknown Charges from a Tripole

[Ryan Sandoval]

Homework Statement

Written Problem: Summing the Electric Field Three point charges q1, q2, and q3 are placed along a straight vertical line to create a “tripole”. At point P, which is directly to the right of q1, the net electric field is exactly zero. We also know that q1 = 1 μC.
b) Write a expressions for the x and y components of the electric field at point P ONLY from q1.
c) Write a expressions for the x and y components of the electric field at point P ONLY from q2.
d) Write a expressions for the x and y components of the electric field at point P ONLY from q3.
e) Using the previous parts, and the fact that the Electric Field is zero at P, solve for both q2 and q3.
f) A charge of value q4 = 1 μC is placed at point P. What is the force on charge q4?

Homework Equations

E[/B] = (kq/(r^2))r

The Attempt at a Solution

x = 0.01m , H = 0.03m , /r₂³ = 2.826(10^-6)m^2 ,/r₃³ = 3.1623(10^-5)m^2
x component of E = k[(q1/x^2) - (xq2/r₂³)+(xq3/r₃³)]=0
y component of E = k[(xq2/r₂³) - (Hq3/r₃³)] = 0
To solve for q2 and q3 I set the two equations together, as well as solving for q2 and q3 and using substitution to find their values.
The most logical answers I found were
q2 = -0.042μC
q3 = 15.8 μC

Plugging in those values of q2 and q3 do not give me a net electric field of zero.

If anyone can confirm that my components are correct, and if they are it must just be my algebra. If not I need some assistance! Thank you

 

[Ryan Sandoval]

q3 is also given as positive

 

[kuruman]

I agree with your value for q3, but not your value for q2. This indicates that your method is correct, but you went astray with the numerical calculation somewhere. Recheck your substitutions and your signs.

 

[Ryan Sandoval]

I agree with your value for q3, but not your value for q2. This indicates that your method is correct, but you went astray with the numerical calculation somewhere. Recheck your substitutions and your signs.

Awesome thank you! That dang algebra.