P 19.a

Three point charges Q1, Q2, and  Q3 are located as shown below:

If the charges are Q₁ = +6.00 mC, Q₂ = -2.00 mC, and Q₃ = -4.00 mC , find the electric field at the origin. Provide both the magnitude and direction of the electric field.

       E₁ = k Q₁ /r₁² = (8.99 x 10⁹ N m² /C²) (6.00 x 10^-6 C)/ (0.200 m )² = 1349 x 10³ N/C

       E₂ = k Q₂ /r₂² = (8.99 x 10⁹ N m² /C²) (2.00 x 10^-6 C)/ (0.150 m )² = 799 x 10³ N/C

       E₃ = k Q₃ /r₃² = (8.99 x 10⁹ N m² /C²) (4.00 x 10^-6 C)/ (0.250 m )² = 575 x 10³ N/C

      E_1x= 1349 x 10³ N/C

      E_1y= 0 N/C

      E_2x= 799 x 10³ N/C

      E_2y= 0 N/C

      E_3x= 0 N/C

      E_3y= - 575 x 10³ N/C

      E_totx= 2148 x 10³ N/C                                                E_tot = 2224 x 10³ N/C                                               

      E_toty= - 575 N/C                                                         q = tan^-1 (E_toty / E_totx) = -15.0 degrees