Question

A charge of 1.52E-9 C is placed at the origin, and a charge of 4.18E-9 C is placed at x = 1.69 m. Find the position at which a third charge of 3.03E-9 C can be placed so that the net electrostatic force on it is zero.

Answer 1

k = 8.99x10^9N-m^2/C^2

What they are asking is where is the field = 0 .It doesn't matter what the third charge is, if the field is zero then the force is zero.

Let x be the distance from the -4.50nC charge so (0.60 + x) is the distance to the other charge since the zero field is located outside of the two charges not between them

Now we only need to deal with the field

So we have k*q1/(1.69 - x)^2 = k*q2/x^2

So 4.18nC*x^2 = 1.52nC*(1.69 - x)^2
=> 1.6583 = (1.69 - x)/x
=> x = 0.6357 m