Answer to Question #185213 in Field Theory for Esmail

Question

A point charge Q1 = 10C is at the origin, and a second charge Q2 = -5C is placed on the y￾axis at y = 1m. What is the total electric field at the point P with coordinates x=2m, y=1m?

Answer 1

Answer

Electric field due to Q1

$E_1=\frac{kQ1}{|r-r'|^3}(r-r') \\=\frac{9\times10^9\times10}{(\sqrt{5}^3)}(-2i-j) \\=4.02\times10^{10}(-2i-j) N/C$

$=-(8.04i+4.02j) \times10^{10}N/C$

Electric field due to Q2

$E_2=\frac{kQ2}{|r-r'|^3}(r-r') \\=\frac{9\times10^9\times10}{({2}^3)}(-2i) \\=2.28\times10^{10}(-i) N/C$

So total electric field at this point

$E=E_1+E_2\\=-(10.32i +4.02j)\times10^{10}N/C$