(Solved): A line charge of linear charge density is uniformly distributed on the y-axis from y=a to y= ...

A line charge of linear charge density $$?$$ is uniformly distributed on the $$y$$-axis from $$y=?a$$ to $$y=+a$$. The electric field along the $$x$$-axis a distance $$x$$ from the origin is $$\vec{E}=\frac{?}{2?{?}_0}\frac{a}{x\sqrt{x^2+a^2}}\hat{i}$$ where $${?}_0=8.85\times 10^{?12}{\mathrm{C}}^2/\mathrm{N}?\mathrm{m}$$ For this question, use variables for a and $$?$$. A line charge is not the same charge distribution as a point charge. If all of the charge in this line charge were concentrated into a single point charge at the origin, it should not produce the same magnitude electric field as the line charge. At what distance along the $$x$$-axis from the line charge (in terms of the length a and to three decimal places) is the magnitude of its electric field within $$1\%$$ of the magnitude of the field produced by an equivalent point charge? At this distance, there is effectively no difference between the two charge distributions in terms of measured values. Use the following method to describe your answer: Suppose you found that a distance of $$13.562$$ a from the line charge is the location where the two fields are within $$1\%$$ of each other. You would enter $$13.562$$ as your answer.