Finding charge given the electric field at origin is zero

[paulie]

Homework Statement

Given that we have q1 = -4nC on the y-axis at y=0.60m. q2 on the y-axis at y= -1.20m. What must be the sign and magnitude of q2 be for the net electric field at the origin to be:
a. Zero
b. 50 N/C

Homework Equations

E=KQ/R²

The Attempt at a Solution

I used: E_T = E₁ + E₂

Since E_T = 0 ; rearranging the equation: E₁ = - E₂

Both K can be canceled out leaving us with: Q₁ / R₁² = - Q₂ / R₂²

Then, Q₂ = - Q₁ (R₂²) / R₁²

Substituting the values: Q₂ = - (-4x10^-9)(1.20m)² / (0.60m)²

Equals 1.6x10^-8 Coulombs, but in my test, my prof corrected and added negative sign on the answer. Am I doing something wrong?

 

[gneill]

With charges and their fields it can be tricky accounting for all the signs and geometric factors affecting the relative field directions. Getting it right strictly by the algebra is tedious and error prone. A better approach is to make a diagram of the scenario and sketch in the charge locations and the field vectors for the positions of interest. In that way it is a simple matter to see by inspection what the charge signs need to be.

In this problem you have a -4 nC charge on the positive y-axis, so you know that at the origin its field vector will be "upwards", pointing along the positive y-axis towards that charge. In order for the net field at the origin to be zero, whatever charge you place below the x-axis must result in a field that opposes that. That should tell you the charge's sign right away.