Hello!
Using the equation for the electric field produced by a source charge:
[tex]E = \frac{kq}{r^2}[/tex]
E = Electric Field Strength ( 2.86 × 10⁵ N/C)
k = Coulomb's Constant ( 8.99 × 10⁹ Nm²/C²)
q = Charge of source charge (3 μC = 0.000003 C)
r = distance of test charge from source charge (m²)
We can rearrange the equation to solve for distance to make plugging in values easier. (Isolate for 'r').
[tex]Er^2 = kq\\\\r^2 = \frac{kq}{E}\\\\r = \sqrt{\frac{kq}{E}}[/tex]
Plug in the given values.
[tex]r = \sqrt{\frac{(8.99*10^9)(3*10^{-6})}{(2.86*10^5)}} = \boxed{0.307 m}[/tex]
