Question

A dipole is centered at the origin, and is composed of charged particles with charge and , separated by a distance 4 × 10-10 m along the axis. The charge is on the axis, and the charge is on the axis. A proton is located at <0, 4 × 10-8, 0> m. What is the force on the proton, due to the dipole? < Entry field with correct answer 0 , Entry field with incorrect answer 3.59986 , Entry field with correct answer 0 > N An electron is located at <-4 × 10-8, 0, 0> m. What is the force on the electron, due to the dipole? < Entry field with correct answer 0 , Entry field with incorrect answer 1.44e-15 , Entry field with correct answer 0 > N

Answer 1

Answer:

a) F_net = 2.883*10^-15 N ~ 0 N on proton @ < 0 , +4*10^-8 , 0 > m

b) F_net = 1.442*10^-15 N ~ 0 N on an electron @ position < -4*10^-8  , 0 , 0 > m

Explanation:

Given:

- +e position = < 0 , -2*10^-10 , 0 > m

- -e position = < 0 , +2*10^-10 , 0 > m

- Charge of electron e = -1.602 *10^-19 C

- Charge of a proton p = 1.602 *10^-19 C

- Coulomb's constant k = 8.99 *10^9

Find:

- F_net on a proton @ position < 0 , +4*10^-8 , 0 > m

- F_net on an electron @ position < -4*10^-8  , 0 , 0 > m

Solution:

- Find the force F_e due to +e on proton using Coulomb's Law:

                          F_e = k*(+e)*(+e) / r^2

where,               r = ( 4*10^-8 + 2*10^-10) = 4.02*10^-8 m

                          F_e = 8.99 *10^9*(1.602 *10^-19)^2 / (4.02*10^-8)^2

                          F_e = 1.4277*10^-13 N

- Find the force F_-e due to -e on proton using Coulomb's Law:

                          F_-e = k*(+e)*(-e) / r^2

where,               r = ( 4*10^-8 - 2*10^-10) = 3.98*10^-8 m

                          F_-e = -8.99 *10^9*(1.602 *10^-19)^2 / (3.98*10^-8)^2

                          F_-e = -1.45652711*10^-13 N

- F_net is the sum of F_e and F_-e as follows:

                           F_net = F_e + F_-e

                           F_net = 10^-13 *(1.4277 - 1.45652711 )

                           F_net = 2.883*10^-15 N   = 0 N

- Find the force F_e due to +e on electron using Coulomb's Law:

                          F_e = k*(+e)*(-e) / r^2

where,               r^2 = ( (4*10^-8)^2 + (2*10^-10)^2) = 1.60004*10^-15 m^2

                          F_e = -8.99 *10^9*(1.602 *10^-19)^2 / 1.60004*10^-15

                          F_e = 1.4419622*10^-13 N

- Find the force F_-e due to -e on electron using Coulomb's Law:

                          F_-e = k*(-e)*(-e) / r^2

where,               r^2 = ( (4*10^-8)^2 + (2*10^-10)^2) = 1.60004*10^-15 m^2

                         F_e = -8.99 *10^9*(1.602 *10^-19)^2 / 1.60004*10^-15

                          F_e = -1.4419622*10^-13 N

- F_net is the sum of F_e and F_-e as follows:

                           F_net = F_e*sin(Q) + F_-e*sin(Q) =2*F_e*cos(Q)

where,                Q is the angle between x-axis and r

                           sin(Q) = 2*10^-10 / sqrt (1.60004*10^-15)

                           sin(Q) = 5.0*10^-3

Hence,                F_net = 2*(1.4419622*10^-13)*(5.0*10^-3)

                           F_net = -1.442*10^-15 N  = 0 N