Answer to Question #125810 in Field Theory for Gabby Thayer

Question

Two 15 nC charges are at (0, -10 cm) and (0, 10 cm) on the y-axis as shown. What is the strength of the electric field at a point 50 cm away on the x-axis?

Answer 1

The total strength of the electric field

$$E=E_1\cos\theta+E_2\cos\theta=2E_1\cos\theta$$ $$\cos\theta=\frac{50}{\sqrt{50^2+10^2}}=\frac{5}{\sqrt{26}}=0.98$$ $$E_1=k\frac{q}{r^2}=9\times 10^9\frac{15\times 10^{-9}}{0.5^2+0.1^2}=519\:\rm N/C$$ $$E=2\times 519\times 0.98=1018\:\rm N/C$$