A + 5.0 C charge is located at the origin.A -13.0 C charge is placed at x = 1.0 m.At what finite location(s)on the x axis will the electric field be equal to zero?

Question

Quizplus · Accepted Answer

The electric field at any point on the x-axis due to these two charges is given by:
E = kq1/(x^2) - kq2/(x-1)^2
where k is the Coulomb constant, q1= +5.0C and q2 = -13.0C.
For the electric field to be zero at any point on x-axis, we need to solve the above equation for x. This is not a trivial problem to solve analytically, but we can use numerical methods to find the root of this equation. By doing so, we find that there are two finite locations where electric field is zero, both of which are closer to the positive charge (+5C) than the negative charge (-13C). Therefore, the best choice is C: not in between, but closer to the positive particle.

A + 50 C Charge Is Located at the Origin