Calculate the magnitude and direction of the Coulomb force on each of the three

Question

Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in the figure below.
6.00 µC                            P                               -2.00 µC
--O-----------------------------------------------------------O--                                        | <-------3.00 cm--------------><--------------2.0 cm------->
a) Calculate the magnitude and direction of the electric field at the position of P.
b) Calculate the magnitude and direction of the electric potential at the position of P.
c) If -3.00 µC charge is brought to the P point from the infinity, find the electric force and it's direction. Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in the figure below.
6.00 µC                            P                               -2.00 µC
--O-----------------------------------------------------------O--                                        | <-------3.00 cm--------------><--------------2.0 cm------->
a) Calculate the magnitude and direction of the electric field at the position of P.
b) Calculate the magnitude and direction of the electric potential at the position of P.
c) If -3.00 µC charge is brought to the P point from the infinity, find the electric force and it's direction.

Explanation / Answer

a) electric field at point p due to charge Q-1 = 6 µC            E_1 = k q_1 / r^2                    = ( 9*10^9 ) ( 6*10^ -6 ) / 0.03^2   = 6*10^ 7 N / C    electric field at point P due to charge q_2    = -2 µC            E_2 = k q_2 / r^2                    = ( 9*10^9 ) ( 2*10^ -6 ) / 0.02^2   = 9*10^ 7 N / C    magnitude of electric field at point P               E = E_1 + E _2   =     15*10^ 7 N /C     direction is toward q_2          b)          electric potential V_1 =   6*0.03*10^ 7   = 0.18*10^ 7 V                                     V_2 =    0.18*10^ 7 electric potential at point P                         V = V_1 + V_2 = 0.36*10^ 7 V c) force between q _1 and q_3 is            F_1 = k q_1q_3 / r^2                    = ( 9*10^9 ) ( 6*10^ -6 )(3*10^ -6) / 0.03^2                      = 180 N     force between q_2   and q_3            F_2 =    k q_2 q_3 / r^2                    = ( 9*10^9 ) ( 2*10^ -6 )(3*10^ -6) / 0.02^2                      = 135 N net force on q_3 due to q_1 and q_2             F = F_1 - F_2   = 180 - 135 = 45 N    towards   q_1                    = ( 9*10^9 ) ( 2*10^ -6 ) / 0.02^2   = 9*10^ 7 N / C    magnitude of electric field at point P               E = E_1 + E _2   =     15*10^ 7 N /C     direction is toward q_2          b)          electric potential V_1 =   6*0.03*10^ 7   = 0.18*10^ 7 V                                     V_2 =    0.18*10^ 7 electric potential at point P                         V = V_1 + V_2 = 0.36*10^ 7 V c) force between q _1 and q_3 is            F_1 = k q_1q_3 / r^2                    = ( 9*10^9 ) ( 6*10^ -6 )(3*10^ -6) / 0.03^2                      = 180 N     force between q_2   and q_3            F_2 =    k q_2 q_3 / r^2                    = ( 9*10^9 ) ( 2*10^ -6 )(3*10^ -6) / 0.02^2                      = 135 N net force on q_3 due to q_1 and q_2             F = F_1 - F_2   = 180 - 135 = 45 N    towards   q_1                    = ( 9*10^9 ) ( 6*10^ -6 )(3*10^ -6) / 0.03^2                      = 180 N     force between q_2   and q_3            F_2 =    k q_2 q_3 / r^2                    = ( 9*10^9 ) ( 2*10^ -6 )(3*10^ -6) / 0.02^2                      = 135 N net force on q_3 due to q_1 and q_2             F = F_1 - F_2   = 180 - 135 = 45 N    towards   q_1                    = ( 9*10^9 ) ( 2*10^ -6 )(3*10^ -6) / 0.02^2                      = 135 N net force on q_3 due to q_1 and q_2             F = F_1 - F_2   = 180 - 135 = 45 N    towards   q_1

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