2 charges located in the x-y plane

[Londonfish]

Homework Statement

Consider 2 charges located in the x-y plane; q₁ of magnitude 5 mC (millicoulombs) is located at the origin, and q₂ of unknown magnitude is located at (x,y) = (0.1, 0) (in metres). The electric field E at position (0.03, 0.05) is found to be entirely in the +y direction (i.e. the x-component is zero). Determine the sign of charge q₁ and the magnitude and sign of charge q₂.

Homework Equations

|q| = 5mC (microCoulombs)

F= qE ; q= charge, E= electric Field
E(r) = ƩE_i(r)
=1/(4*pi*ε_°)*Ʃ(r-r_i)*q_i/(r-r_i)³

The Attempt at a Solution

E₁(for one charge)= 1/(4*pi*ε_°)*q₁/r²
= 1/(4*pi*ε_°)* (0.000005 C)/0.0015m
E= 2.996*10⁷

Then I went and did,
E=1/(4*pi*ε_°)[(q₁/r²)+q₂/(r-r₂)²]
rearrange for q₂ and,
q₂= [E(4*pi*ε_°)+(r²/q₁)](r-r₂)²
q₂= -29.9997 C. (This seems way to high to be correct)

So q₁ is positive to make E in the + y direction.

 

[SammyS]

If q₂ is negative, and q₁ is positive, then at a location having it's x coordinate between that of the two charges, the electric field would definitely have a non-zero x component.

 

[Londonfish]

Thanks for that. What do you think of the other part of the problem? I'm not quite sure if I'm missing something or did something wrong.